Setup
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Data preparation
220 parsing failures.
row col expected actual
301 -- date like %m/%d/%y Jun-07
302 -- date like %m/%d/%y Jun-07
303 -- date like %m/%d/%y Jun-07
304 -- date like %m/%d/%y Jun-07
305 -- date like %m/%d/%y Jun-07
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80 parsing failures.
row col expected actual
21 -- date like %m/%d/%y Jun-12
22 -- date like %m/%d/%y Jun-12
23 -- date like %m/%d/%y Jun-12
24 -- date like %m/%d/%y Jun-12
25 -- date like %m/%d/%y Jun-12
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See problems(...) for more details.
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Analysis plan
For all studies we conduct exploratory factor analyses using Pearson correlations to find minimum residual solutions.
For each study, we first examine maximal unrotated and rotated solutions. To determine the maximum number of factors to extract, we use the following rule of thumb: With \(p\) observations per participant, we can extract a maximum of \(k\) factors, where \((p-k)*2 > p+k\), i.e., \(k < p/3\). Thus, with 40 mental capacity items, we can extract a maximum of 13 factors.
To determine how many factors to retain, we use the following preset retention criteria, considering the unrotated maximal solution (unless otherwise noted):
- Each factor must have an eigenvalue >1.0.
- Each factor must individually account for >5% of the total variance in the maximal model.
- After rotation, each factor must be the dominant factor (i.e., the factor with the highest factor loading) for ≥1 mental capacity item.
We then examine and interpret varimax-rotated solutions, extracting only the number of factors that meet these criteria.
Study 1
Study information:
- Design: 2 conditions (beetle, robot), 3-point response scale, “decide what to do” and “have intentions”
- Population: adults
- Date conducted: 2016-07-06 (MTurk)
Demographics
Joining, by = c("character", "min_age", "max_age", "median_age", "mean_age", "sd_age")
joining character vector and factor, coercing into character vector
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Exploratory factor analysis
Step 1: Run maximal EFA (without and with rotation)
Parallel analysis suggests that the number of factors = 4 and the number of components = 4

Factor Analysis using method = minres
Call: fa(r = d1_all, nfactors = 13, rotate = "none", fm = "minres",
cor = chosenCorType)
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR2 MR3 MR4 MR5 MR6 MR7 MR8 MR11 MR9 MR10 MR12 MR13 h2 u2
angry 0.66 0.09 0.03 0.00 -0.02 -0.23 -0.08 -0.13 0.05 0.01 0.04 -0.02 0.21 0.57 0.427
beliefs 0.39 0.45 0.16 -0.06 0.23 -0.06 0.44 0.10 0.03 0.13 -0.14 -0.01 -0.01 0.68 0.323
calm 0.69 -0.07 0.13 -0.08 0.08 -0.04 -0.04 0.10 0.08 0.10 0.08 0.12 0.05 0.56 0.445
choices 0.24 0.22 0.48 0.12 0.25 0.03 -0.20 -0.09 -0.14 -0.19 -0.12 -0.18 0.14 0.59 0.413
communicating -0.02 0.51 0.45 0.11 -0.27 -0.14 -0.19 0.16 -0.01 0.10 -0.08 0.08 -0.11 0.67 0.333
computations -0.48 0.74 0.20 0.00 -0.14 0.01 0.05 0.02 0.05 -0.05 -0.03 0.00 0.08 0.84 0.155
conscious 0.34 0.00 0.42 0.22 0.20 0.07 -0.01 -0.14 0.00 -0.14 -0.15 0.07 0.04 0.45 0.545
depressed 0.74 0.27 -0.08 -0.34 -0.01 0.06 -0.09 -0.16 0.14 -0.04 0.02 0.00 -0.05 0.81 0.191
depth 0.14 0.14 0.46 0.31 -0.06 0.29 0.02 -0.20 -0.05 -0.01 -0.07 0.01 0.05 0.48 0.515
desires 0.64 -0.09 0.14 0.03 0.11 0.07 0.00 0.03 -0.24 0.27 0.11 -0.16 -0.02 0.63 0.370
disrespected 0.65 0.31 -0.18 -0.07 -0.01 0.11 -0.07 -0.13 0.03 0.04 -0.04 0.02 -0.06 0.60 0.403
embarrassed 0.56 0.44 -0.38 0.32 -0.01 -0.04 -0.02 0.18 0.02 -0.14 0.18 0.05 0.01 0.84 0.160
emo_recog 0.27 0.41 0.18 -0.11 0.17 0.04 0.28 0.03 -0.03 -0.17 -0.06 0.16 -0.16 0.49 0.513
fear 0.79 -0.35 0.20 -0.06 -0.24 -0.22 0.12 -0.06 -0.03 -0.08 0.02 -0.02 0.00 0.91 0.087
free_will 0.19 0.17 0.40 0.16 0.36 -0.19 -0.19 -0.12 -0.14 -0.08 0.07 -0.03 0.09 0.51 0.492
goal 0.32 0.16 0.32 0.11 0.13 -0.08 0.18 0.02 -0.10 0.01 0.09 -0.15 0.05 0.35 0.654
guilt 0.67 0.48 -0.38 0.31 -0.03 -0.04 0.00 -0.07 -0.02 0.03 -0.09 -0.02 -0.02 0.93 0.070
happy 0.76 0.20 -0.02 -0.38 0.04 -0.03 -0.15 -0.08 0.05 0.04 -0.08 0.05 -0.01 0.81 0.189
hungry 0.65 -0.64 -0.01 0.15 0.09 0.08 -0.02 0.07 0.00 0.04 0.02 0.01 -0.02 0.89 0.112
intentions 0.05 0.54 0.33 0.00 0.13 -0.20 0.06 0.05 0.08 0.05 0.30 -0.13 -0.05 0.59 0.415
joy 0.77 0.26 -0.10 -0.33 -0.06 0.14 -0.04 0.09 -0.10 0.02 0.05 0.10 0.05 0.84 0.162
love 0.73 0.31 -0.02 -0.19 0.07 0.22 0.04 -0.01 -0.07 0.03 0.01 -0.12 -0.07 0.74 0.262
morality 0.20 0.50 0.20 -0.10 0.04 0.03 0.22 0.10 0.09 -0.02 0.05 -0.15 0.01 0.43 0.570
nauseated 0.67 -0.26 0.16 -0.03 -0.06 0.13 -0.09 0.11 -0.14 0.07 0.02 -0.02 0.05 0.61 0.391
odors 0.50 -0.37 0.20 0.26 0.10 0.19 0.00 0.08 0.03 -0.09 0.06 0.22 0.02 0.61 0.391
pain 0.71 -0.45 0.09 0.12 -0.06 -0.08 -0.09 0.13 0.15 0.10 -0.10 -0.02 0.03 0.81 0.192
personality 0.35 0.42 0.12 -0.14 0.20 0.03 0.19 0.17 -0.11 0.03 -0.12 0.15 0.11 0.50 0.501
pleasure 0.72 -0.10 0.04 -0.12 -0.13 0.23 0.01 0.20 0.01 -0.27 -0.09 -0.13 -0.06 0.76 0.242
pride 0.66 0.41 -0.12 -0.19 0.01 -0.02 0.05 -0.08 0.00 0.06 0.19 0.01 0.12 0.72 0.282
reasoning 0.21 0.30 0.49 0.12 0.11 -0.15 -0.16 -0.08 -0.20 -0.11 0.01 0.22 -0.06 0.56 0.438
recognizing -0.07 0.65 0.47 0.03 -0.19 -0.04 -0.09 0.18 -0.01 0.12 -0.07 0.04 0.03 0.75 0.251
remembering -0.01 0.54 0.44 0.04 -0.08 0.05 -0.14 0.05 -0.04 -0.01 0.04 -0.14 -0.24 0.60 0.396
safe 0.72 -0.27 0.24 0.03 0.10 -0.11 0.12 -0.09 -0.05 0.00 -0.04 0.08 -0.10 0.72 0.283
seeing 0.24 0.03 0.45 0.33 -0.08 0.27 -0.02 -0.15 0.14 -0.02 0.06 -0.01 0.00 0.50 0.498
self_aware 0.36 0.11 0.33 0.09 0.31 -0.14 -0.05 -0.01 0.17 0.10 0.05 0.07 -0.22 0.47 0.529
self_restraint 0.33 0.36 0.20 -0.07 0.23 0.02 0.09 0.07 0.15 -0.06 -0.09 0.03 0.17 0.42 0.582
sounds 0.18 0.09 0.45 0.21 -0.28 0.22 0.06 -0.17 -0.02 0.06 0.18 0.06 0.00 0.48 0.519
temperature 0.21 0.06 0.44 0.28 -0.14 0.35 0.17 -0.18 0.17 0.10 0.11 0.04 0.03 0.58 0.423
thoughts 0.45 0.15 0.31 -0.06 0.36 -0.11 -0.14 0.13 0.21 -0.10 0.04 -0.09 0.00 0.57 0.433
tired 0.71 -0.29 0.20 0.11 -0.07 0.04 -0.03 0.07 0.06 0.07 -0.07 -0.08 0.12 0.69 0.313
com
angry 1.7
beliefs 4.4
calm 1.4
choices 5.1
communicating 3.8
computations 2.1
conscious 4.1
depressed 2.0
depth 3.7
desires 2.2
disrespected 1.9
embarrassed 4.2
emo_recog 5.3
fear 2.1
free_will 5.4
goal 4.9
guilt 3.1
happy 1.8
hungry 2.2
intentions 3.2
joy 1.9
love 1.9
morality 2.8
nauseated 1.8
odors 4.0
pain 2.2
personality 4.9
pleasure 2.0
pride 2.3
reasoning 4.3
recognizing 2.5
remembering 2.8
safe 1.8
seeing 3.9
self_aware 5.2
self_restraint 4.9
sounds 4.4
temperature 5.2
thoughts 4.6
tired 1.8
MR1 MR2 MR3 MR4 MR5 MR6 MR7 MR8 MR11 MR9 MR10 MR12 MR13
SS loadings 10.58 5.08 3.45 1.31 1.07 0.82 0.73 0.53 0.43 0.41 0.40 0.39 0.34
Proportion Var 0.26 0.13 0.09 0.03 0.03 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01
Cumulative Var 0.26 0.39 0.48 0.51 0.54 0.56 0.58 0.59 0.60 0.61 0.62 0.63 0.64
Proportion Explained 0.41 0.20 0.13 0.05 0.04 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.01
Cumulative Proportion 0.41 0.61 0.75 0.80 0.84 0.87 0.90 0.92 0.94 0.96 0.97 0.99 1.00
Mean item complexity = 3.2
Test of the hypothesis that 13 factors are sufficient.
The degrees of freedom for the null model are 780 and the objective function was 27.45 with Chi Square of 5073.12
The degrees of freedom for the model are 338 and the objective function was 2.29
The root mean square of the residuals (RMSR) is 0.02
The df corrected root mean square of the residuals is 0.03
The harmonic number of observations is 196 with the empirical chi square 118.47 with prob < 1
The total number of observations was 200 with MLE Chi Square = 403.84 with prob < 0.008
Tucker Lewis Index of factoring reliability = 0.963
RMSEA index = 0.042 and the 90 % confidence intervals are 0.017 0.042
BIC = -1386.99
Fit based upon off diagonal values = 1
Measures of factor score adequacy
MR1 MR2 MR3 MR4 MR5 MR6 MR7 MR8 MR11 MR9 MR10 MR12
Correlation of scores with factors 0.99 0.98 0.96 0.93 0.87 0.85 0.82 0.80 0.73 0.76 0.75 0.71
Multiple R square of scores with factors 0.98 0.96 0.92 0.86 0.76 0.72 0.67 0.64 0.54 0.57 0.56 0.50
Minimum correlation of possible factor scores 0.96 0.92 0.83 0.72 0.52 0.44 0.34 0.27 0.08 0.15 0.12 0.01
MR13
Correlation of scores with factors 0.68
Multiple R square of scores with factors 0.47
Minimum correlation of possible factor scores -0.07
Factor Analysis using method = minres
Call: fa(r = d1_all, nfactors = 13, rotate = "none", fm = "minres",
cor = chosenCorType)
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR2 MR3 MR4 MR5 MR6 MR7 MR8 MR11 MR9 MR10 MR12 MR13 h2 u2
angry 0.66 0.09 0.03 0.00 -0.02 -0.23 -0.08 -0.13 0.05 0.01 0.04 -0.02 0.21 0.57 0.427
beliefs 0.39 0.45 0.16 -0.06 0.23 -0.06 0.44 0.10 0.03 0.13 -0.14 -0.01 -0.01 0.68 0.323
calm 0.69 -0.07 0.13 -0.08 0.08 -0.04 -0.04 0.10 0.08 0.10 0.08 0.12 0.05 0.56 0.445
choices 0.24 0.22 0.48 0.12 0.25 0.03 -0.20 -0.09 -0.14 -0.19 -0.12 -0.18 0.14 0.59 0.413
communicating -0.02 0.51 0.45 0.11 -0.27 -0.14 -0.19 0.16 -0.01 0.10 -0.08 0.08 -0.11 0.67 0.333
computations -0.48 0.74 0.20 0.00 -0.14 0.01 0.05 0.02 0.05 -0.05 -0.03 0.00 0.08 0.84 0.155
conscious 0.34 0.00 0.42 0.22 0.20 0.07 -0.01 -0.14 0.00 -0.14 -0.15 0.07 0.04 0.45 0.545
depressed 0.74 0.27 -0.08 -0.34 -0.01 0.06 -0.09 -0.16 0.14 -0.04 0.02 0.00 -0.05 0.81 0.191
depth 0.14 0.14 0.46 0.31 -0.06 0.29 0.02 -0.20 -0.05 -0.01 -0.07 0.01 0.05 0.48 0.515
desires 0.64 -0.09 0.14 0.03 0.11 0.07 0.00 0.03 -0.24 0.27 0.11 -0.16 -0.02 0.63 0.370
disrespected 0.65 0.31 -0.18 -0.07 -0.01 0.11 -0.07 -0.13 0.03 0.04 -0.04 0.02 -0.06 0.60 0.403
embarrassed 0.56 0.44 -0.38 0.32 -0.01 -0.04 -0.02 0.18 0.02 -0.14 0.18 0.05 0.01 0.84 0.160
emo_recog 0.27 0.41 0.18 -0.11 0.17 0.04 0.28 0.03 -0.03 -0.17 -0.06 0.16 -0.16 0.49 0.513
fear 0.79 -0.35 0.20 -0.06 -0.24 -0.22 0.12 -0.06 -0.03 -0.08 0.02 -0.02 0.00 0.91 0.087
free_will 0.19 0.17 0.40 0.16 0.36 -0.19 -0.19 -0.12 -0.14 -0.08 0.07 -0.03 0.09 0.51 0.492
goal 0.32 0.16 0.32 0.11 0.13 -0.08 0.18 0.02 -0.10 0.01 0.09 -0.15 0.05 0.35 0.654
guilt 0.67 0.48 -0.38 0.31 -0.03 -0.04 0.00 -0.07 -0.02 0.03 -0.09 -0.02 -0.02 0.93 0.070
happy 0.76 0.20 -0.02 -0.38 0.04 -0.03 -0.15 -0.08 0.05 0.04 -0.08 0.05 -0.01 0.81 0.189
hungry 0.65 -0.64 -0.01 0.15 0.09 0.08 -0.02 0.07 0.00 0.04 0.02 0.01 -0.02 0.89 0.112
intentions 0.05 0.54 0.33 0.00 0.13 -0.20 0.06 0.05 0.08 0.05 0.30 -0.13 -0.05 0.59 0.415
joy 0.77 0.26 -0.10 -0.33 -0.06 0.14 -0.04 0.09 -0.10 0.02 0.05 0.10 0.05 0.84 0.162
love 0.73 0.31 -0.02 -0.19 0.07 0.22 0.04 -0.01 -0.07 0.03 0.01 -0.12 -0.07 0.74 0.262
morality 0.20 0.50 0.20 -0.10 0.04 0.03 0.22 0.10 0.09 -0.02 0.05 -0.15 0.01 0.43 0.570
nauseated 0.67 -0.26 0.16 -0.03 -0.06 0.13 -0.09 0.11 -0.14 0.07 0.02 -0.02 0.05 0.61 0.391
odors 0.50 -0.37 0.20 0.26 0.10 0.19 0.00 0.08 0.03 -0.09 0.06 0.22 0.02 0.61 0.391
pain 0.71 -0.45 0.09 0.12 -0.06 -0.08 -0.09 0.13 0.15 0.10 -0.10 -0.02 0.03 0.81 0.192
personality 0.35 0.42 0.12 -0.14 0.20 0.03 0.19 0.17 -0.11 0.03 -0.12 0.15 0.11 0.50 0.501
pleasure 0.72 -0.10 0.04 -0.12 -0.13 0.23 0.01 0.20 0.01 -0.27 -0.09 -0.13 -0.06 0.76 0.242
pride 0.66 0.41 -0.12 -0.19 0.01 -0.02 0.05 -0.08 0.00 0.06 0.19 0.01 0.12 0.72 0.282
reasoning 0.21 0.30 0.49 0.12 0.11 -0.15 -0.16 -0.08 -0.20 -0.11 0.01 0.22 -0.06 0.56 0.438
recognizing -0.07 0.65 0.47 0.03 -0.19 -0.04 -0.09 0.18 -0.01 0.12 -0.07 0.04 0.03 0.75 0.251
remembering -0.01 0.54 0.44 0.04 -0.08 0.05 -0.14 0.05 -0.04 -0.01 0.04 -0.14 -0.24 0.60 0.396
safe 0.72 -0.27 0.24 0.03 0.10 -0.11 0.12 -0.09 -0.05 0.00 -0.04 0.08 -0.10 0.72 0.283
seeing 0.24 0.03 0.45 0.33 -0.08 0.27 -0.02 -0.15 0.14 -0.02 0.06 -0.01 0.00 0.50 0.498
self_aware 0.36 0.11 0.33 0.09 0.31 -0.14 -0.05 -0.01 0.17 0.10 0.05 0.07 -0.22 0.47 0.529
self_restraint 0.33 0.36 0.20 -0.07 0.23 0.02 0.09 0.07 0.15 -0.06 -0.09 0.03 0.17 0.42 0.582
sounds 0.18 0.09 0.45 0.21 -0.28 0.22 0.06 -0.17 -0.02 0.06 0.18 0.06 0.00 0.48 0.519
temperature 0.21 0.06 0.44 0.28 -0.14 0.35 0.17 -0.18 0.17 0.10 0.11 0.04 0.03 0.58 0.423
thoughts 0.45 0.15 0.31 -0.06 0.36 -0.11 -0.14 0.13 0.21 -0.10 0.04 -0.09 0.00 0.57 0.433
tired 0.71 -0.29 0.20 0.11 -0.07 0.04 -0.03 0.07 0.06 0.07 -0.07 -0.08 0.12 0.69 0.313
com
angry 1.7
beliefs 4.4
calm 1.4
choices 5.1
communicating 3.8
computations 2.1
conscious 4.1
depressed 2.0
depth 3.7
desires 2.2
disrespected 1.9
embarrassed 4.2
emo_recog 5.3
fear 2.1
free_will 5.4
goal 4.9
guilt 3.1
happy 1.8
hungry 2.2
intentions 3.2
joy 1.9
love 1.9
morality 2.8
nauseated 1.8
odors 4.0
pain 2.2
personality 4.9
pleasure 2.0
pride 2.3
reasoning 4.3
recognizing 2.5
remembering 2.8
safe 1.8
seeing 3.9
self_aware 5.2
self_restraint 4.9
sounds 4.4
temperature 5.2
thoughts 4.6
tired 1.8
MR1 MR2 MR3 MR4 MR5 MR6 MR7 MR8 MR11 MR9 MR10 MR12 MR13
SS loadings 10.58 5.08 3.45 1.31 1.07 0.82 0.73 0.53 0.43 0.41 0.40 0.39 0.34
Proportion Var 0.26 0.13 0.09 0.03 0.03 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01
Cumulative Var 0.26 0.39 0.48 0.51 0.54 0.56 0.58 0.59 0.60 0.61 0.62 0.63 0.64
Proportion Explained 0.41 0.20 0.13 0.05 0.04 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.01
Cumulative Proportion 0.41 0.61 0.75 0.80 0.84 0.87 0.90 0.92 0.94 0.96 0.97 0.99 1.00
Mean item complexity = 3.2
Test of the hypothesis that 13 factors are sufficient.
The degrees of freedom for the null model are 780 and the objective function was 27.45 with Chi Square of 5073.12
The degrees of freedom for the model are 338 and the objective function was 2.29
The root mean square of the residuals (RMSR) is 0.02
The df corrected root mean square of the residuals is 0.03
The harmonic number of observations is 196 with the empirical chi square 118.47 with prob < 1
The total number of observations was 200 with MLE Chi Square = 403.84 with prob < 0.008
Tucker Lewis Index of factoring reliability = 0.963
RMSEA index = 0.042 and the 90 % confidence intervals are 0.017 0.042
BIC = -1386.99
Fit based upon off diagonal values = 1
Measures of factor score adequacy
MR1 MR2 MR3 MR4 MR5 MR6 MR7 MR8 MR11 MR9 MR10 MR12
Correlation of scores with factors 0.99 0.98 0.96 0.93 0.87 0.85 0.82 0.80 0.73 0.76 0.75 0.71
Multiple R square of scores with factors 0.98 0.96 0.92 0.86 0.76 0.72 0.67 0.64 0.54 0.57 0.56 0.50
Minimum correlation of possible factor scores 0.96 0.92 0.83 0.72 0.52 0.44 0.34 0.27 0.08 0.15 0.12 0.01
MR13
Correlation of scores with factors 0.68
Multiple R square of scores with factors 0.47
Minimum correlation of possible factor scores -0.07
[1] 4
[1] 4
Step 2: Run EFA with varimax rotation
Factor Analysis using method = minres
Call: fa(r = d1_all, nfactors = nfactors_d1_all, rotate = chosenRotType,
fm = "minres", cor = chosenCorType)
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR2 MR3 MR4 h2 u2 com
angry 0.40 0.49 0.14 0.15 0.44 0.56 2.3
beliefs -0.02 0.52 0.31 0.06 0.37 0.63 1.7
calm 0.55 0.43 0.15 -0.01 0.51 0.49 2.1
choices 0.09 0.17 0.56 -0.07 0.36 0.64 1.3
communicating -0.32 0.18 0.56 -0.01 0.45 0.55 1.8
computations -0.83 0.09 0.34 0.01 0.81 0.19 1.4
conscious 0.32 0.07 0.50 0.00 0.36 0.64 1.7
depressed 0.30 0.80 0.01 0.03 0.72 0.28 1.3
depth 0.09 -0.04 0.59 0.10 0.37 0.63 1.1
desires 0.54 0.33 0.19 0.06 0.45 0.55 2.0
disrespected 0.24 0.66 0.03 0.27 0.56 0.44 1.6
embarrassed 0.09 0.52 0.04 0.67 0.73 0.27 1.9
emo_recog -0.08 0.45 0.29 -0.01 0.29 0.71 1.8
fear 0.77 0.31 0.12 -0.04 0.70 0.30 1.4
free_will 0.08 0.12 0.48 -0.05 0.25 0.75 1.2
goal 0.16 0.22 0.42 0.03 0.25 0.75 1.9
guilt 0.15 0.62 0.06 0.65 0.83 0.17 2.1
happy 0.37 0.79 0.02 -0.07 0.76 0.24 1.4
hungry 0.94 -0.02 -0.07 0.09 0.89 0.11 1.0
intentions -0.31 0.32 0.45 -0.02 0.40 0.60 2.6
joy 0.33 0.80 0.00 0.06 0.75 0.25 1.4
love 0.29 0.73 0.13 0.11 0.66 0.34 1.4
morality -0.19 0.44 0.33 0.01 0.34 0.66 2.2
nauseated 0.67 0.27 0.14 -0.02 0.54 0.46 1.4
odors 0.67 -0.04 0.23 0.12 0.52 0.48 1.3
pain 0.83 0.14 0.06 0.07 0.71 0.29 1.1
personality -0.03 0.52 0.24 0.01 0.33 0.67 1.4
pleasure 0.57 0.44 0.07 0.05 0.53 0.47 1.9
pride 0.16 0.77 0.06 0.20 0.67 0.33 1.2
reasoning 0.01 0.20 0.59 -0.05 0.39 0.61 1.2
recognizing -0.44 0.25 0.59 -0.05 0.61 0.39 2.3
remembering -0.33 0.23 0.56 -0.05 0.48 0.52 2.0
safe 0.72 0.27 0.22 -0.03 0.65 0.35 1.5
seeing 0.23 -0.05 0.57 0.11 0.40 0.60 1.4
self_aware 0.24 0.23 0.40 -0.04 0.27 0.73 2.3
self_restraint 0.01 0.44 0.32 0.00 0.30 0.70 1.8
sounds 0.13 0.00 0.52 0.04 0.29 0.71 1.1
temperature 0.18 -0.03 0.54 0.10 0.34 0.66 1.3
thoughts 0.25 0.39 0.35 -0.11 0.35 0.65 2.9
tired 0.73 0.22 0.22 0.06 0.63 0.37 1.4
MR1 MR2 MR3 MR4
SS loadings 7.32 6.89 4.89 1.14
Proportion Var 0.18 0.17 0.12 0.03
Cumulative Var 0.18 0.36 0.48 0.51
Proportion Explained 0.36 0.34 0.24 0.06
Cumulative Proportion 0.36 0.70 0.94 1.00
Mean item complexity = 1.7
Test of the hypothesis that 4 factors are sufficient.
The degrees of freedom for the null model are 780 and the objective function was 27.45 with Chi Square of 5073.12
The degrees of freedom for the model are 626 and the objective function was 5.74
The root mean square of the residuals (RMSR) is 0.05
The df corrected root mean square of the residuals is 0.05
The harmonic number of observations is 196 with the empirical chi square 628.12 with prob < 0.47
The total number of observations was 200 with MLE Chi Square = 1045.75 with prob < 1.3e-23
Tucker Lewis Index of factoring reliability = 0.876
RMSEA index = 0.064 and the 90 % confidence intervals are 0.052 NA
BIC = -2270.99
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy
MR1 MR2 MR3 MR4
Correlation of scores with factors 0.98 0.96 0.94 0.89
Multiple R square of scores with factors 0.96 0.93 0.89 0.79
Minimum correlation of possible factor scores 0.92 0.86 0.79 0.58
back to TOC
Study 2
Study information:
- Design: 2 conditions (beetle, robot), 3-point response scale, “decide what to do” and “have intentions”
- Population: 7-9yo children
- Date conducted: June - December 2016
Demographics
Joining, by = c("character", "min_age", "max_age", "median_age", "mean_age", "sd_age")
joining character vector and factor, coercing into character vector
back to TOC
Exploratory factor analysis
Step 1: Run maximal EFA (without and with rotation)
Parallel analysis suggests that the number of factors = 3 and the number of components = 3

Factor Analysis using method = minres
Call: fa(r = d2_all, nfactors = 13, rotate = "none", fm = "minres",
cor = chosenCorType)
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR2 MR3 MR4 MR5 MR6 MR7 MR8 MR9 MR11 MR10 MR12 MR13 h2 u2 com
angry 0.59 -0.05 -0.08 -0.07 0.13 0.00 0.15 0.04 -0.02 0.03 -0.05 0.07 -0.02 0.41 0.59 1.4
beliefs 0.47 0.32 -0.04 -0.05 0.16 0.00 0.08 -0.17 -0.01 -0.15 0.08 0.03 0.09 0.43 0.57 2.9
calm 0.55 0.04 0.00 -0.02 -0.10 0.01 -0.09 -0.10 0.01 0.16 0.04 -0.16 0.15 0.40 0.60 1.7
choices 0.41 0.09 0.23 -0.31 0.31 0.08 -0.10 -0.20 0.02 -0.08 -0.10 0.20 -0.02 0.53 0.47 5.4
communicating 0.04 0.29 0.16 0.10 -0.16 0.29 0.06 0.15 0.26 0.06 0.08 0.17 -0.14 0.38 0.62 6.7
computations -0.16 0.80 0.08 0.06 0.07 -0.01 0.06 -0.16 0.06 0.13 0.05 0.09 0.04 0.73 0.27 1.3
conscious 0.35 0.09 0.47 0.01 -0.12 0.29 0.09 0.16 -0.27 0.02 0.07 -0.09 0.07 0.57 0.43 4.3
depressed 0.70 0.04 -0.15 0.06 -0.02 0.08 -0.12 0.12 0.15 0.15 -0.14 0.11 0.06 0.63 0.37 1.7
depth 0.11 0.19 0.42 0.24 0.14 -0.09 0.11 -0.08 0.06 -0.06 0.13 -0.22 -0.03 0.40 0.60 4.2
desires 0.54 -0.10 -0.09 -0.07 0.06 0.13 0.09 -0.11 0.03 -0.14 0.00 -0.07 0.11 0.39 0.61 1.8
disrespected 0.67 0.13 -0.14 -0.01 0.14 0.08 -0.11 0.09 -0.19 -0.03 0.10 0.01 -0.03 0.58 0.42 1.7
embarrassed 0.50 0.16 -0.30 0.17 0.24 0.13 0.37 0.03 -0.09 -0.01 -0.07 0.04 0.00 0.63 0.37 4.1
emo_recog 0.25 0.54 0.03 0.08 0.03 -0.10 0.07 0.27 -0.05 0.02 0.07 0.10 -0.01 0.47 0.53 2.3
fear 0.63 -0.30 0.05 -0.04 -0.15 0.09 0.16 0.14 0.29 -0.03 -0.15 -0.19 -0.04 0.71 0.29 2.9
free_will 0.48 0.04 0.29 -0.21 0.15 0.10 -0.12 -0.25 0.06 -0.14 -0.05 -0.08 -0.04 0.51 0.49 3.7
goal 0.28 0.36 0.00 -0.14 0.01 0.03 0.05 -0.01 0.13 0.11 -0.11 -0.03 0.28 0.35 0.65 4.1
guilt 0.54 0.21 -0.16 0.22 0.14 -0.01 0.23 -0.14 -0.08 -0.05 0.06 -0.20 -0.05 0.56 0.44 3.2
happy 0.69 0.25 -0.20 0.09 -0.18 0.18 -0.10 -0.08 -0.01 0.02 0.07 0.01 -0.14 0.69 0.31 2.0
hungry 0.51 -0.70 0.13 0.13 0.10 -0.04 -0.04 -0.02 0.00 -0.02 -0.02 0.04 -0.03 0.80 0.20 2.1
intentions 0.27 0.44 0.20 -0.09 0.28 0.00 -0.08 -0.09 -0.01 0.14 -0.12 -0.13 -0.27 0.54 0.46 5.0
joy 0.68 0.17 -0.26 0.05 -0.12 0.10 -0.17 -0.06 -0.02 0.03 0.13 0.08 -0.01 0.64 0.36 1.9
love 0.58 0.16 -0.19 0.20 0.02 0.03 -0.13 0.09 -0.14 -0.11 0.02 -0.04 0.03 0.51 0.49 2.1
morality 0.38 0.45 -0.05 -0.04 -0.01 -0.49 -0.01 0.21 0.06 -0.13 0.17 -0.02 -0.07 0.68 0.32 3.9
nauseated 0.37 -0.38 0.03 0.24 0.14 -0.09 0.10 0.00 0.14 -0.02 -0.07 0.11 0.04 0.41 0.59 3.9
odors 0.25 -0.55 0.29 0.00 0.07 0.00 0.16 -0.10 0.12 0.13 0.33 0.06 -0.10 0.64 0.36 3.6
pain 0.56 -0.57 0.13 0.01 0.10 -0.08 -0.13 -0.01 -0.02 -0.08 0.07 0.05 0.10 0.71 0.29 2.5
personality 0.48 0.38 0.03 -0.05 0.22 -0.14 0.17 0.05 0.09 0.01 -0.01 0.10 0.18 0.52 0.48 3.6
pleasure 0.58 0.17 -0.17 -0.02 -0.29 -0.02 -0.17 -0.17 0.07 0.02 0.09 -0.13 0.09 0.57 0.43 2.6
pride 0.63 0.31 -0.28 0.04 -0.07 0.01 0.00 -0.04 -0.04 0.02 -0.08 0.00 -0.08 0.60 0.40 2.0
reasoning 0.18 0.27 0.36 -0.08 -0.04 0.19 -0.08 0.09 0.17 -0.17 0.11 -0.06 0.22 0.41 0.59 6.1
recognizing 0.14 0.33 0.17 0.07 0.00 -0.06 0.10 0.02 0.22 0.06 0.15 -0.09 0.12 0.27 0.73 4.6
remembering -0.03 0.54 0.23 0.06 -0.03 0.15 -0.06 0.07 0.18 -0.34 -0.12 0.14 -0.11 0.58 0.42 3.2
safe 0.63 0.00 0.31 -0.16 -0.35 -0.25 0.17 -0.10 -0.10 0.03 -0.13 0.09 -0.07 0.77 0.23 3.3
seeing -0.09 0.08 0.21 -0.12 0.00 0.14 -0.13 0.21 0.03 -0.15 0.20 -0.05 -0.17 0.25 0.75 7.8
self_aware 0.23 0.19 0.46 -0.20 0.02 0.16 0.12 0.23 -0.29 0.04 -0.05 -0.05 0.04 0.53 0.47 4.6
self_restraint 0.29 0.21 0.12 -0.20 0.32 -0.14 -0.29 0.18 0.09 0.23 -0.08 -0.18 -0.05 0.53 0.47 8.1
sounds -0.08 0.03 0.33 -0.12 -0.03 0.21 0.14 -0.03 0.12 0.19 0.22 0.09 -0.05 0.31 0.69 5.1
temperature -0.09 0.27 0.55 0.52 -0.04 -0.08 -0.16 -0.09 -0.04 0.02 -0.12 -0.01 0.03 0.71 0.29 3.0
thoughts 0.57 0.10 0.18 -0.12 -0.06 -0.05 -0.15 0.03 -0.08 0.03 0.08 0.13 0.13 0.46 0.54 1.9
tired 0.45 -0.28 0.03 0.22 0.09 -0.01 -0.08 0.24 0.03 0.17 -0.04 0.13 -0.02 0.45 0.55 3.8
MR1 MR2 MR3 MR4 MR5 MR6 MR7 MR8 MR9 MR11 MR10 MR12 MR13
SS loadings 8.11 4.24 2.17 0.96 0.91 0.82 0.77 0.70 0.63 0.53 0.52 0.47 0.46
Proportion Var 0.20 0.11 0.05 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01
Cumulative Var 0.20 0.31 0.36 0.39 0.41 0.43 0.45 0.47 0.48 0.50 0.51 0.52 0.53
Proportion Explained 0.38 0.20 0.10 0.05 0.04 0.04 0.04 0.03 0.03 0.02 0.02 0.02 0.02
Cumulative Proportion 0.38 0.58 0.68 0.73 0.77 0.81 0.84 0.88 0.91 0.93 0.96 0.98 1.00
Mean item complexity = 3.5
Test of the hypothesis that 13 factors are sufficient.
The degrees of freedom for the null model are 780 and the objective function was 17.08 with Chi Square of 3157.08
The degrees of freedom for the model are 338 and the objective function was 1.73
The root mean square of the residuals (RMSR) is 0.02
The df corrected root mean square of the residuals is 0.03
The harmonic number of observations is 198 with the empirical chi square 155.46 with prob < 1
The total number of observations was 200 with MLE Chi Square = 304.73 with prob < 0.9
Tucker Lewis Index of factoring reliability = 1.034
RMSEA index = 0.01 and the 90 % confidence intervals are NA 0.012
BIC = -1486.1
Fit based upon off diagonal values = 0.99
Measures of factor score adequacy
MR1 MR2 MR3 MR4 MR5 MR6 MR7 MR8 MR9 MR11 MR10 MR12
Correlation of scores with factors 0.98 0.96 0.92 0.84 0.84 0.83 0.81 0.78 0.77 0.73 0.74 0.71
Multiple R square of scores with factors 0.95 0.93 0.84 0.71 0.70 0.68 0.65 0.61 0.59 0.53 0.55 0.51
Minimum correlation of possible factor scores 0.91 0.85 0.68 0.42 0.40 0.36 0.30 0.22 0.18 0.06 0.10 0.01
MR13
Correlation of scores with factors 0.69
Multiple R square of scores with factors 0.48
Minimum correlation of possible factor scores -0.04
Factor Analysis using method = minres
Call: fa(r = d2_all, nfactors = 13, rotate = "none", fm = "minres",
cor = chosenCorType)
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR2 MR3 MR4 MR5 MR6 MR7 MR8 MR9 MR11 MR10 MR12 MR13 h2 u2 com
angry 0.59 -0.05 -0.08 -0.07 0.13 0.00 0.15 0.04 -0.02 0.03 -0.05 0.07 -0.02 0.41 0.59 1.4
beliefs 0.47 0.32 -0.04 -0.05 0.16 0.00 0.08 -0.17 -0.01 -0.15 0.08 0.03 0.09 0.43 0.57 2.9
calm 0.55 0.04 0.00 -0.02 -0.10 0.01 -0.09 -0.10 0.01 0.16 0.04 -0.16 0.15 0.40 0.60 1.7
choices 0.41 0.09 0.23 -0.31 0.31 0.08 -0.10 -0.20 0.02 -0.08 -0.10 0.20 -0.02 0.53 0.47 5.4
communicating 0.04 0.29 0.16 0.10 -0.16 0.29 0.06 0.15 0.26 0.06 0.08 0.17 -0.14 0.38 0.62 6.7
computations -0.16 0.80 0.08 0.06 0.07 -0.01 0.06 -0.16 0.06 0.13 0.05 0.09 0.04 0.73 0.27 1.3
conscious 0.35 0.09 0.47 0.01 -0.12 0.29 0.09 0.16 -0.27 0.02 0.07 -0.09 0.07 0.57 0.43 4.3
depressed 0.70 0.04 -0.15 0.06 -0.02 0.08 -0.12 0.12 0.15 0.15 -0.14 0.11 0.06 0.63 0.37 1.7
depth 0.11 0.19 0.42 0.24 0.14 -0.09 0.11 -0.08 0.06 -0.06 0.13 -0.22 -0.03 0.40 0.60 4.2
desires 0.54 -0.10 -0.09 -0.07 0.06 0.13 0.09 -0.11 0.03 -0.14 0.00 -0.07 0.11 0.39 0.61 1.8
disrespected 0.67 0.13 -0.14 -0.01 0.14 0.08 -0.11 0.09 -0.19 -0.03 0.10 0.01 -0.03 0.58 0.42 1.7
embarrassed 0.50 0.16 -0.30 0.17 0.24 0.13 0.37 0.03 -0.09 -0.01 -0.07 0.04 0.00 0.63 0.37 4.1
emo_recog 0.25 0.54 0.03 0.08 0.03 -0.10 0.07 0.27 -0.05 0.02 0.07 0.10 -0.01 0.47 0.53 2.3
fear 0.63 -0.30 0.05 -0.04 -0.15 0.09 0.16 0.14 0.29 -0.03 -0.15 -0.19 -0.04 0.71 0.29 2.9
free_will 0.48 0.04 0.29 -0.21 0.15 0.10 -0.12 -0.25 0.06 -0.14 -0.05 -0.08 -0.04 0.51 0.49 3.7
goal 0.28 0.36 0.00 -0.14 0.01 0.03 0.05 -0.01 0.13 0.11 -0.11 -0.03 0.28 0.35 0.65 4.1
guilt 0.54 0.21 -0.16 0.22 0.14 -0.01 0.23 -0.14 -0.08 -0.05 0.06 -0.20 -0.05 0.56 0.44 3.2
happy 0.69 0.25 -0.20 0.09 -0.18 0.18 -0.10 -0.08 -0.01 0.02 0.07 0.01 -0.14 0.69 0.31 2.0
hungry 0.51 -0.70 0.13 0.13 0.10 -0.04 -0.04 -0.02 0.00 -0.02 -0.02 0.04 -0.03 0.80 0.20 2.1
intentions 0.27 0.44 0.20 -0.09 0.28 0.00 -0.08 -0.09 -0.01 0.14 -0.12 -0.13 -0.27 0.54 0.46 5.0
joy 0.68 0.17 -0.26 0.05 -0.12 0.10 -0.17 -0.06 -0.02 0.03 0.13 0.08 -0.01 0.64 0.36 1.9
love 0.58 0.16 -0.19 0.20 0.02 0.03 -0.13 0.09 -0.14 -0.11 0.02 -0.04 0.03 0.51 0.49 2.1
morality 0.38 0.45 -0.05 -0.04 -0.01 -0.49 -0.01 0.21 0.06 -0.13 0.17 -0.02 -0.07 0.68 0.32 3.9
nauseated 0.37 -0.38 0.03 0.24 0.14 -0.09 0.10 0.00 0.14 -0.02 -0.07 0.11 0.04 0.41 0.59 3.9
odors 0.25 -0.55 0.29 0.00 0.07 0.00 0.16 -0.10 0.12 0.13 0.33 0.06 -0.10 0.64 0.36 3.6
pain 0.56 -0.57 0.13 0.01 0.10 -0.08 -0.13 -0.01 -0.02 -0.08 0.07 0.05 0.10 0.71 0.29 2.5
personality 0.48 0.38 0.03 -0.05 0.22 -0.14 0.17 0.05 0.09 0.01 -0.01 0.10 0.18 0.52 0.48 3.6
pleasure 0.58 0.17 -0.17 -0.02 -0.29 -0.02 -0.17 -0.17 0.07 0.02 0.09 -0.13 0.09 0.57 0.43 2.6
pride 0.63 0.31 -0.28 0.04 -0.07 0.01 0.00 -0.04 -0.04 0.02 -0.08 0.00 -0.08 0.60 0.40 2.0
reasoning 0.18 0.27 0.36 -0.08 -0.04 0.19 -0.08 0.09 0.17 -0.17 0.11 -0.06 0.22 0.41 0.59 6.1
recognizing 0.14 0.33 0.17 0.07 0.00 -0.06 0.10 0.02 0.22 0.06 0.15 -0.09 0.12 0.27 0.73 4.6
remembering -0.03 0.54 0.23 0.06 -0.03 0.15 -0.06 0.07 0.18 -0.34 -0.12 0.14 -0.11 0.58 0.42 3.2
safe 0.63 0.00 0.31 -0.16 -0.35 -0.25 0.17 -0.10 -0.10 0.03 -0.13 0.09 -0.07 0.77 0.23 3.3
seeing -0.09 0.08 0.21 -0.12 0.00 0.14 -0.13 0.21 0.03 -0.15 0.20 -0.05 -0.17 0.25 0.75 7.8
self_aware 0.23 0.19 0.46 -0.20 0.02 0.16 0.12 0.23 -0.29 0.04 -0.05 -0.05 0.04 0.53 0.47 4.6
self_restraint 0.29 0.21 0.12 -0.20 0.32 -0.14 -0.29 0.18 0.09 0.23 -0.08 -0.18 -0.05 0.53 0.47 8.1
sounds -0.08 0.03 0.33 -0.12 -0.03 0.21 0.14 -0.03 0.12 0.19 0.22 0.09 -0.05 0.31 0.69 5.1
temperature -0.09 0.27 0.55 0.52 -0.04 -0.08 -0.16 -0.09 -0.04 0.02 -0.12 -0.01 0.03 0.71 0.29 3.0
thoughts 0.57 0.10 0.18 -0.12 -0.06 -0.05 -0.15 0.03 -0.08 0.03 0.08 0.13 0.13 0.46 0.54 1.9
tired 0.45 -0.28 0.03 0.22 0.09 -0.01 -0.08 0.24 0.03 0.17 -0.04 0.13 -0.02 0.45 0.55 3.8
MR1 MR2 MR3 MR4 MR5 MR6 MR7 MR8 MR9 MR11 MR10 MR12 MR13
SS loadings 8.11 4.24 2.17 0.96 0.91 0.82 0.77 0.70 0.63 0.53 0.52 0.47 0.46
Proportion Var 0.20 0.11 0.05 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01
Cumulative Var 0.20 0.31 0.36 0.39 0.41 0.43 0.45 0.47 0.48 0.50 0.51 0.52 0.53
Proportion Explained 0.38 0.20 0.10 0.05 0.04 0.04 0.04 0.03 0.03 0.02 0.02 0.02 0.02
Cumulative Proportion 0.38 0.58 0.68 0.73 0.77 0.81 0.84 0.88 0.91 0.93 0.96 0.98 1.00
Mean item complexity = 3.5
Test of the hypothesis that 13 factors are sufficient.
The degrees of freedom for the null model are 780 and the objective function was 17.08 with Chi Square of 3157.08
The degrees of freedom for the model are 338 and the objective function was 1.73
The root mean square of the residuals (RMSR) is 0.02
The df corrected root mean square of the residuals is 0.03
The harmonic number of observations is 198 with the empirical chi square 155.46 with prob < 1
The total number of observations was 200 with MLE Chi Square = 304.73 with prob < 0.9
Tucker Lewis Index of factoring reliability = 1.034
RMSEA index = 0.01 and the 90 % confidence intervals are NA 0.012
BIC = -1486.1
Fit based upon off diagonal values = 0.99
Measures of factor score adequacy
MR1 MR2 MR3 MR4 MR5 MR6 MR7 MR8 MR9 MR11 MR10 MR12
Correlation of scores with factors 0.98 0.96 0.92 0.84 0.84 0.83 0.81 0.78 0.77 0.73 0.74 0.71
Multiple R square of scores with factors 0.95 0.93 0.84 0.71 0.70 0.68 0.65 0.61 0.59 0.53 0.55 0.51
Minimum correlation of possible factor scores 0.91 0.85 0.68 0.42 0.40 0.36 0.30 0.22 0.18 0.06 0.10 0.01
MR13
Correlation of scores with factors 0.69
Multiple R square of scores with factors 0.48
Minimum correlation of possible factor scores -0.04
[1] 3
[1] 3
Step 2: Run EFA with varimax rotation
Factor Analysis using method = minres
Call: fa(r = d2_all, nfactors = nfactors_d2_all, rotate = chosenRotType,
fm = "minres", cor = chosenCorType)
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR2 MR3 h2 u2 com
angry 0.50 0.31 0.05 0.351 0.65 1.7
beliefs 0.53 -0.04 0.22 0.330 0.67 1.3
calm 0.48 0.22 0.13 0.298 0.70 1.6
choices 0.28 0.19 0.36 0.241 0.76 2.4
communicating 0.09 -0.19 0.26 0.108 0.89 2.1
computations 0.14 -0.71 0.34 0.638 0.36 1.5
conscious 0.17 0.20 0.49 0.307 0.69 1.6
depressed 0.66 0.26 0.03 0.505 0.49 1.3
depth 0.02 0.01 0.45 0.199 0.80 1.0
desires 0.44 0.32 0.03 0.303 0.70 1.8
disrespected 0.67 0.19 0.10 0.488 0.51 1.2
embarrassed 0.57 0.04 -0.06 0.330 0.67 1.0
emo_recog 0.40 -0.31 0.29 0.341 0.66 2.7
fear 0.39 0.53 0.06 0.438 0.56 1.9
free_will 0.31 0.28 0.40 0.335 0.67 2.7
goal 0.37 -0.17 0.22 0.217 0.78 2.1
guilt 0.59 0.05 0.06 0.351 0.65 1.0
happy 0.76 0.07 0.05 0.582 0.42 1.0
hungry 0.12 0.87 -0.07 0.777 0.22 1.1
intentions 0.32 -0.18 0.41 0.297 0.70 2.3
joy 0.75 0.12 -0.04 0.575 0.42 1.1
love 0.63 0.11 0.00 0.414 0.59 1.1
morality 0.47 -0.18 0.20 0.293 0.71 1.7
nauseated 0.16 0.51 -0.06 0.288 0.71 1.2
odors -0.10 0.63 0.11 0.424 0.58 1.1
pain 0.21 0.79 0.01 0.663 0.34 1.1
personality 0.51 -0.06 0.31 0.359 0.64 1.7
pleasure 0.62 0.09 0.02 0.393 0.61 1.0
pride 0.77 -0.04 -0.02 0.602 0.40 1.0
reasoning 0.12 -0.04 0.49 0.259 0.74 1.1
recognizing 0.18 -0.17 0.32 0.159 0.84 2.1
remembering 0.10 -0.40 0.39 0.318 0.68 2.1
safe 0.42 0.33 0.31 0.381 0.62 2.8
seeing -0.13 -0.05 0.23 0.072 0.93 1.7
self_aware 0.11 0.06 0.52 0.288 0.71 1.1
self_restraint 0.26 0.02 0.28 0.145 0.85 2.0
sounds -0.17 0.01 0.33 0.140 0.86 1.5
temperature -0.12 -0.13 0.42 0.212 0.79 1.4
thoughts 0.46 0.24 0.32 0.367 0.63 2.4
tired 0.27 0.46 -0.01 0.286 0.71 1.6
MR1 MR2 MR3
SS loadings 7.05 4.19 2.84
Proportion Var 0.18 0.10 0.07
Cumulative Var 0.18 0.28 0.35
Proportion Explained 0.50 0.30 0.20
Cumulative Proportion 0.50 0.80 1.00
Mean item complexity = 1.6
Test of the hypothesis that 3 factors are sufficient.
The degrees of freedom for the null model are 780 and the objective function was 17.08 with Chi Square of 3157.08
The degrees of freedom for the model are 663 and the objective function was 4.77
The root mean square of the residuals (RMSR) is 0.05
The df corrected root mean square of the residuals is 0.06
The harmonic number of observations is 198 with the empirical chi square 801.93 with prob < 0.00016
The total number of observations was 200 with MLE Chi Square = 871.71 with prob < 8.1e-08
Tucker Lewis Index of factoring reliability = 0.895
RMSEA index = 0.047 and the 90 % confidence intervals are 0.032 0.047
BIC = -2641.07
Fit based upon off diagonal values = 0.95
Measures of factor score adequacy
MR1 MR2 MR3
Correlation of scores with factors 0.96 0.95 0.88
Multiple R square of scores with factors 0.91 0.90 0.78
Minimum correlation of possible factor scores 0.83 0.80 0.55
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Study 3
Study information:
- Design: 7 conditions (beetle, robot, …) + 2 follow-up conditions, 3-point response scale, “decide what to do” and “have intentions”
- Population: 7-9yo children
- Date conducted: January - June 2017
Exploratory factor analysis
Step 1: Run maximal EFA (without and with rotation)
Parallel analysis suggests that the number of factors = 3 and the number of components = 3

Factor Analysis using method = minres
Call: fa(r = d3_all, nfactors = 13, rotate = "none", fm = "minres",
cor = chosenCorType)
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR5 MR2 MR4 MR6 MR10 MR8 MR9 MR11 MR3 MR7 MR12 MR13 h2 u2 com
angry 0.69 0.32 -0.17 0.06 0.03 -0.15 0.33 -0.33 0.03 0.12 0.11 0.07 -0.01 0.88 0.122 3.0
choices 0.39 0.34 0.20 0.10 0.38 -0.15 0.17 0.24 0.12 0.08 0.13 -0.24 -0.14 0.69 0.308 6.9
conscious 0.38 0.25 0.27 -0.03 0.12 -0.06 0.21 0.12 0.08 0.02 0.12 0.30 0.12 0.48 0.519 5.7
depressed 0.51 0.40 -0.09 0.30 -0.10 0.25 0.27 -0.15 0.16 -0.02 0.05 -0.04 -0.04 0.72 0.283 4.6
depth 0.45 -0.01 0.89 0.01 -0.02 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 1.00 0.005 1.5
disrespected 0.40 0.35 -0.08 0.33 -0.14 0.36 0.23 0.04 0.09 0.11 0.04 -0.04 0.16 0.65 0.352 5.8
embarrassed 0.39 0.29 0.05 0.39 -0.15 0.17 0.15 0.08 -0.35 0.04 0.13 -0.05 0.01 0.61 0.388 5.4
fear 0.91 -0.08 -0.22 0.08 0.01 0.00 -0.01 0.00 0.00 0.31 0.00 0.00 0.00 1.00 0.005 1.4
guilt 0.32 0.31 -0.20 0.35 -0.18 0.07 0.32 0.13 -0.36 0.19 -0.02 0.00 -0.14 0.71 0.294 7.5
happy 0.54 0.42 -0.16 0.14 -0.06 0.09 -0.04 -0.06 0.17 0.03 0.00 -0.10 -0.20 0.62 0.383 3.1
hungry 0.81 0.16 -0.14 -0.49 -0.10 0.00 -0.04 0.01 -0.01 0.11 0.14 0.00 0.00 0.98 0.020 2.0
love 0.56 0.14 -0.22 0.23 -0.06 0.31 0.05 0.32 -0.01 0.08 -0.02 0.19 -0.04 0.68 0.321 3.8
nauseated 0.43 0.16 -0.07 -0.20 0.14 0.28 0.21 0.02 0.12 0.05 0.14 -0.24 0.24 0.55 0.448 5.8
odors 0.67 0.19 -0.14 -0.42 0.04 0.02 0.06 -0.01 -0.01 0.24 -0.46 0.00 0.00 0.95 0.054 3.2
pain 0.91 -0.03 -0.17 0.01 0.02 0.00 0.00 0.00 0.00 -0.37 -0.01 0.00 0.00 1.00 0.005 1.4
pride 0.54 0.60 -0.16 0.43 -0.20 -0.07 -0.17 0.01 0.01 -0.04 -0.05 0.00 0.03 0.95 0.051 3.5
reasoning 0.26 0.29 0.32 -0.09 0.28 -0.24 0.18 0.39 0.25 0.23 -0.03 0.07 0.00 0.70 0.301 7.9
remembering 0.18 0.29 0.19 0.04 0.43 -0.31 0.24 0.23 -0.24 0.09 0.11 -0.05 0.15 0.65 0.348 6.7
temperature 0.30 0.35 0.30 0.00 0.73 0.12 -0.18 -0.10 -0.06 0.09 0.06 0.03 -0.01 0.90 0.097 2.6
tired 0.70 0.21 -0.01 -0.01 0.06 0.18 0.07 0.19 0.14 0.11 0.13 0.13 -0.07 0.67 0.325 1.9
MR1 MR5 MR2 MR4 MR6 MR10 MR8 MR9 MR11 MR3 MR7 MR12 MR13
SS loadings 6.17 1.74 1.44 1.21 1.12 0.65 0.64 0.58 0.50 0.47 0.35 0.29 0.21
Proportion Var 0.31 0.09 0.07 0.06 0.06 0.03 0.03 0.03 0.02 0.02 0.02 0.01 0.01
Cumulative Var 0.31 0.40 0.47 0.53 0.58 0.62 0.65 0.68 0.70 0.73 0.74 0.76 0.77
Proportion Explained 0.40 0.11 0.09 0.08 0.07 0.04 0.04 0.04 0.03 0.03 0.02 0.02 0.01
Cumulative Proportion 0.40 0.51 0.61 0.69 0.76 0.80 0.84 0.88 0.91 0.94 0.97 0.99 1.00
Mean item complexity = 4.2
Test of the hypothesis that 13 factors are sufficient.
The degrees of freedom for the null model are 190 and the objective function was 11.71 with Chi Square of 1399.04
The degrees of freedom for the model are 8 and the objective function was 0.05
The root mean square of the residuals (RMSR) is 0.01
The df corrected root mean square of the residuals is 0.03
The harmonic number of observations is 128 with the empirical chi square 1.57 with prob < 0.99
The total number of observations was 128 with MLE Chi Square = 5.47 with prob < 0.71
Tucker Lewis Index of factoring reliability = 1.054
RMSEA index = 0 and the 90 % confidence intervals are NA 0.079
BIC = -33.35
Fit based upon off diagonal values = 1
Measures of factor score adequacy
MR1 MR5 MR2 MR4 MR6 MR10 MR8 MR9 MR11 MR3 MR7 MR12
Correlation of scores with factors 1 0.97 1.00 0.98 0.95 0.83 0.88 0.84 0.78 0.99 0.92 0.66
Multiple R square of scores with factors 1 0.94 0.99 0.96 0.89 0.69 0.77 0.71 0.61 0.98 0.84 0.44
Minimum correlation of possible factor scores 1 0.88 0.99 0.91 0.79 0.38 0.54 0.42 0.21 0.96 0.68 -0.13
MR13
Correlation of scores with factors 0.61
Multiple R square of scores with factors 0.37
Minimum correlation of possible factor scores -0.27
Factor Analysis using method = minres
Call: fa(r = d3_all, nfactors = 13, rotate = "none", fm = "minres",
cor = chosenCorType)
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR5 MR2 MR4 MR6 MR10 MR8 MR9 MR11 MR3 MR7 MR12 MR13 h2 u2 com
angry 0.69 0.32 -0.17 0.06 0.03 -0.15 0.33 -0.33 0.03 0.12 0.11 0.07 -0.01 0.88 0.122 3.0
choices 0.39 0.34 0.20 0.10 0.38 -0.15 0.17 0.24 0.12 0.08 0.13 -0.24 -0.14 0.69 0.308 6.9
conscious 0.38 0.25 0.27 -0.03 0.12 -0.06 0.21 0.12 0.08 0.02 0.12 0.30 0.12 0.48 0.519 5.7
depressed 0.51 0.40 -0.09 0.30 -0.10 0.25 0.27 -0.15 0.16 -0.02 0.05 -0.04 -0.04 0.72 0.283 4.6
depth 0.45 -0.01 0.89 0.01 -0.02 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 1.00 0.005 1.5
disrespected 0.40 0.35 -0.08 0.33 -0.14 0.36 0.23 0.04 0.09 0.11 0.04 -0.04 0.16 0.65 0.352 5.8
embarrassed 0.39 0.29 0.05 0.39 -0.15 0.17 0.15 0.08 -0.35 0.04 0.13 -0.05 0.01 0.61 0.388 5.4
fear 0.91 -0.08 -0.22 0.08 0.01 0.00 -0.01 0.00 0.00 0.31 0.00 0.00 0.00 1.00 0.005 1.4
guilt 0.32 0.31 -0.20 0.35 -0.18 0.07 0.32 0.13 -0.36 0.19 -0.02 0.00 -0.14 0.71 0.294 7.5
happy 0.54 0.42 -0.16 0.14 -0.06 0.09 -0.04 -0.06 0.17 0.03 0.00 -0.10 -0.20 0.62 0.383 3.1
hungry 0.81 0.16 -0.14 -0.49 -0.10 0.00 -0.04 0.01 -0.01 0.11 0.14 0.00 0.00 0.98 0.020 2.0
love 0.56 0.14 -0.22 0.23 -0.06 0.31 0.05 0.32 -0.01 0.08 -0.02 0.19 -0.04 0.68 0.321 3.8
nauseated 0.43 0.16 -0.07 -0.20 0.14 0.28 0.21 0.02 0.12 0.05 0.14 -0.24 0.24 0.55 0.448 5.8
odors 0.67 0.19 -0.14 -0.42 0.04 0.02 0.06 -0.01 -0.01 0.24 -0.46 0.00 0.00 0.95 0.054 3.2
pain 0.91 -0.03 -0.17 0.01 0.02 0.00 0.00 0.00 0.00 -0.37 -0.01 0.00 0.00 1.00 0.005 1.4
pride 0.54 0.60 -0.16 0.43 -0.20 -0.07 -0.17 0.01 0.01 -0.04 -0.05 0.00 0.03 0.95 0.051 3.5
reasoning 0.26 0.29 0.32 -0.09 0.28 -0.24 0.18 0.39 0.25 0.23 -0.03 0.07 0.00 0.70 0.301 7.9
remembering 0.18 0.29 0.19 0.04 0.43 -0.31 0.24 0.23 -0.24 0.09 0.11 -0.05 0.15 0.65 0.348 6.7
temperature 0.30 0.35 0.30 0.00 0.73 0.12 -0.18 -0.10 -0.06 0.09 0.06 0.03 -0.01 0.90 0.097 2.6
tired 0.70 0.21 -0.01 -0.01 0.06 0.18 0.07 0.19 0.14 0.11 0.13 0.13 -0.07 0.67 0.325 1.9
MR1 MR5 MR2 MR4 MR6 MR10 MR8 MR9 MR11 MR3 MR7 MR12 MR13
SS loadings 6.17 1.74 1.44 1.21 1.12 0.65 0.64 0.58 0.50 0.47 0.35 0.29 0.21
Proportion Var 0.31 0.09 0.07 0.06 0.06 0.03 0.03 0.03 0.02 0.02 0.02 0.01 0.01
Cumulative Var 0.31 0.40 0.47 0.53 0.58 0.62 0.65 0.68 0.70 0.73 0.74 0.76 0.77
Proportion Explained 0.40 0.11 0.09 0.08 0.07 0.04 0.04 0.04 0.03 0.03 0.02 0.02 0.01
Cumulative Proportion 0.40 0.51 0.61 0.69 0.76 0.80 0.84 0.88 0.91 0.94 0.97 0.99 1.00
Mean item complexity = 4.2
Test of the hypothesis that 13 factors are sufficient.
The degrees of freedom for the null model are 190 and the objective function was 11.71 with Chi Square of 1399.04
The degrees of freedom for the model are 8 and the objective function was 0.05
The root mean square of the residuals (RMSR) is 0.01
The df corrected root mean square of the residuals is 0.03
The harmonic number of observations is 128 with the empirical chi square 1.57 with prob < 0.99
The total number of observations was 128 with MLE Chi Square = 5.47 with prob < 0.71
Tucker Lewis Index of factoring reliability = 1.054
RMSEA index = 0 and the 90 % confidence intervals are NA 0.079
BIC = -33.35
Fit based upon off diagonal values = 1
Measures of factor score adequacy
MR1 MR5 MR2 MR4 MR6 MR10 MR8 MR9 MR11 MR3 MR7 MR12
Correlation of scores with factors 1 0.97 1.00 0.98 0.95 0.83 0.88 0.84 0.78 0.99 0.92 0.66
Multiple R square of scores with factors 1 0.94 0.99 0.96 0.89 0.69 0.77 0.71 0.61 0.98 0.84 0.44
Minimum correlation of possible factor scores 1 0.88 0.99 0.91 0.79 0.38 0.54 0.42 0.21 0.96 0.68 -0.13
MR13
Correlation of scores with factors 0.61
Multiple R square of scores with factors 0.37
Minimum correlation of possible factor scores -0.27
[1] 5
[1] 3
Step 2: Run EFA with varimax rotation
Factor Analysis using method = minres
Call: fa(r = d3_all, nfactors = nfactors_d3_all, rotate = chosenRotType,
fm = "minres", cor = chosenCorType)
Standardized loadings (pattern matrix) based upon correlation matrix
MR2 MR1 MR3 h2 u2 com
angry 0.51 0.54 0.24 0.61 0.39 2.4
choices 0.26 0.14 0.70 0.58 0.42 1.4
conscious 0.18 0.22 0.50 0.33 0.67 1.7
depressed 0.73 0.25 0.13 0.61 0.39 1.3
depth 0.02 0.17 0.50 0.28 0.72 1.2
disrespected 0.70 0.15 0.11 0.52 0.48 1.1
embarrassed 0.65 0.08 0.14 0.45 0.55 1.1
fear 0.42 0.76 0.14 0.77 0.23 1.6
guilt 0.65 0.11 0.05 0.44 0.56 1.1
happy 0.56 0.39 0.14 0.49 0.51 1.9
hungry 0.14 0.91 0.17 0.87 0.13 1.1
love 0.56 0.38 0.06 0.46 0.54 1.8
nauseated 0.19 0.43 0.23 0.27 0.73 2.0
odors 0.11 0.76 0.18 0.63 0.37 1.2
pain 0.38 0.71 0.09 0.66 0.34 1.6
pride 0.74 0.27 0.13 0.63 0.37 1.3
reasoning 0.01 0.13 0.72 0.53 0.47 1.1
remembering 0.09 -0.01 0.65 0.43 0.57 1.0
temperature 0.08 0.13 0.62 0.41 0.59 1.1
tired 0.40 0.56 0.34 0.59 0.41 2.5
MR2 MR1 MR3
SS loadings 3.96 3.88 2.72
Proportion Var 0.20 0.19 0.14
Cumulative Var 0.20 0.39 0.53
Proportion Explained 0.37 0.37 0.26
Cumulative Proportion 0.37 0.74 1.00
Mean item complexity = 1.5
Test of the hypothesis that 3 factors are sufficient.
The degrees of freedom for the null model are 190 and the objective function was 11.71 with Chi Square of 1399.04
The degrees of freedom for the model are 133 and the objective function was 1.75
The root mean square of the residuals (RMSR) is 0.05
The df corrected root mean square of the residuals is 0.05
The harmonic number of observations is 128 with the empirical chi square 101.61 with prob < 0.98
The total number of observations was 128 with MLE Chi Square = 206 with prob < 5.1e-05
Tucker Lewis Index of factoring reliability = 0.912
RMSEA index = 0.073 and the 90 % confidence intervals are 0.047 0.083
BIC = -439.32
Fit based upon off diagonal values = 0.99
Measures of factor score adequacy
MR2 MR1 MR3
Correlation of scores with factors 0.92 0.95 0.90
Multiple R square of scores with factors 0.85 0.90 0.80
Minimum correlation of possible factor scores 0.70 0.80 0.61
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Subscales
Reliability (and intercorrelations - see alpha)
Call: scoreItems(keys = keys.list, items = d3_all, min = 0, max = 1)
(Unstandardized) Alpha:
SOUL BODY MIND
alpha 0.87 0.9 0.8
Standard errors of unstandardized Alpha:
SOUL BODY MIND
ASE 0.036 0.032 0.049
Average item correlation:
SOUL BODY MIND
average.r 0.49 0.57 0.4
Guttman 6* reliability:
SOUL BODY MIND
Lambda.6 0.89 0.92 0.82
Signal/Noise based upon av.r :
SOUL BODY MIND
Signal/Noise 6.8 9.1 4.1
Scale intercorrelations corrected for attenuation
raw correlations below the diagonal, alpha on the diagonal
corrected correlations above the diagonal:
SOUL BODY MIND
SOUL 0.87 0.72 0.37
BODY 0.63 0.90 0.51
MIND 0.31 0.43 0.80
In order to see the item by scale loadings and frequency counts of the data
print with the short option = FALSE
Loading required namespace: GPArotation
Omega
Call: omega(m = d3_all, plot = F)
Alpha: 0.91
G.6: 0.94
Omega Hierarchical: 0.64
Omega H asymptotic: 0.68
Omega Total 0.94
Schmid Leiman Factor loadings greater than 0.2
g F1* F2* F3* h2 u2 p2
angry 0.65 0.30 0.28 0.61 0.39 0.70
choices 0.43 0.62 0.58 0.42 0.31
conscious 0.37 0.42 0.33 0.67 0.42
depressed 0.54 0.56 0.61 0.39 0.49
depth 0.27 0.44 0.28 0.72 0.26
disrespected 0.46 0.55 0.52 0.48 0.41
embarrassed 0.40 0.53 0.45 0.55 0.36
fear 0.71 0.47 0.77 0.23 0.66
guilt 0.40 0.53 0.44 0.56 0.36
happy 0.56 0.39 0.49 0.51 0.63
hungry 0.68 0.63 0.87 0.13 0.53
love 0.52 0.40 0.46 0.54 0.59
nauseated 0.43 0.26 0.27 0.73 0.67
odors 0.58 0.53 0.63 0.37 0.54
pain 0.65 0.45 0.66 0.34 0.64
pride 0.56 0.56 0.63 0.37 0.49
reasoning 0.31 0.66 0.53 0.47 0.18
remembering 0.23 0.61 0.43 0.57 0.12
temperature 0.31 0.56 0.41 0.59 0.23
tired 0.64 0.20 0.31 0.21 0.59 0.41 0.70
With eigenvalues of:
g F1* F2* F3*
5.1 2.0 1.4 2.0
general/max 2.5 max/min = 1.41
mean percent general = 0.46 with sd = 0.18 and cv of 0.39
Explained Common Variance of the general factor = 0.48
The degrees of freedom are 133 and the fit is 1.75
The number of observations was 128 with Chi Square = 206 with prob < 5.1e-05
The root mean square of the residuals is 0.05
The df corrected root mean square of the residuals is 0.05
RMSEA index = 0.073 and the 90 % confidence intervals are 0.047 0.083
BIC = -439.32
Compare this with the adequacy of just a general factor and no group factors
The degrees of freedom for just the general factor are 170 and the fit is 5.09
The number of observations was 128 with Chi Square = 605.34 with prob < 3.7e-50
The root mean square of the residuals is 0.16
The df corrected root mean square of the residuals is 0.17
RMSEA index = 0.149 and the 90 % confidence intervals are 0.129 0.154
BIC = -219.51
Measures of factor score adequacy
g F1* F2* F3*
Correlation of scores with factors 0.82 0.80 0.72 0.85
Multiple R square of scores with factors 0.68 0.64 0.51 0.73
Minimum correlation of factor score estimates 0.35 0.28 0.03 0.45
Total, General and Subset omega for each subset
g F1* F2* F3*
Omega total for total scores and subscales 0.94 0.88 0.90 0.81
Omega general for total scores and subscales 0.64 0.47 0.59 0.20
Omega group for total scores and subscales 0.22 0.41 0.30 0.61
Study 4
Study information:
- Design: 7 conditions (beetle, robot, …) + 2 follow-up conditions (doll, teddy bear), 3-point response scale, “decide what to do” and “have intentions”
- Population: 4-6yo children
- Date conducted: March 2017 - present
Demographics
Joining, by = c("character", "min_age", "max_age", "median_age", "mean_age", "sd_age")
joining character vector and factor, coercing into character vector
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Exploratory factor analysis
Step 1: Run maximal EFA (without and with rotation)
Parallel analysis suggests that the number of factors = 2 and the number of components = 1

Factor Analysis using method = minres
Call: fa(r = d4_all, nfactors = 13, rotate = "none", fm = "minres",
cor = chosenCorType)
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR3 MR5 MR6 MR4 MR7 MR2 MR8 MR10 MR9 MR12 MR11 MR13 h2 u2 com
angry 0.49 0.43 0.31 -0.19 -0.09 -0.17 0.12 -0.42 -0.06 -0.04 0.07 -0.09 0.13 0.83 0.172 5.0
choices 0.33 0.26 0.31 -0.01 -0.04 0.18 0.01 0.14 0.19 -0.02 0.18 -0.03 0.09 0.40 0.598 5.6
conscious 0.26 0.39 0.46 0.42 0.15 -0.25 -0.09 -0.03 -0.02 0.25 -0.08 -0.12 -0.14 0.80 0.199 5.7
depressed 0.46 0.30 0.33 -0.29 0.05 -0.25 0.09 -0.02 0.17 -0.34 0.00 0.16 -0.17 0.77 0.233 6.4
depth 0.29 0.30 0.22 0.25 0.06 0.06 0.03 -0.10 0.47 0.13 -0.12 0.00 0.15 0.58 0.420 4.6
disrespected 0.45 0.39 0.17 -0.04 0.05 -0.12 0.31 -0.03 -0.11 -0.06 0.06 -0.01 0.03 0.52 0.479 3.6
embarrassed 0.53 0.33 -0.27 0.03 0.67 -0.02 0.15 -0.04 -0.02 -0.05 0.00 -0.01 0.00 0.93 0.066 3.0
fear 0.86 -0.05 0.00 0.00 0.01 0.00 -0.51 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.005 1.6
guilt 0.36 0.32 0.17 0.12 0.10 0.25 -0.08 0.05 0.11 -0.16 0.40 -0.05 -0.05 0.56 0.435 5.4
happy 0.53 0.23 0.23 -0.24 0.27 -0.13 0.07 0.29 0.11 0.04 0.01 -0.15 0.17 0.69 0.312 4.7
hungry 0.64 0.45 0.04 -0.34 -0.05 0.36 0.05 -0.05 -0.07 0.12 -0.05 -0.07 -0.08 0.89 0.107 3.4
love 0.50 0.32 0.21 -0.20 0.15 -0.13 -0.03 0.41 0.01 -0.11 -0.13 -0.11 0.00 0.68 0.316 4.4
nauseated 0.86 -0.06 0.00 0.01 -0.02 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.005 1.6
odors 0.55 0.60 -0.30 0.06 -0.39 -0.10 -0.13 0.05 0.02 -0.01 0.01 -0.01 0.01 0.94 0.056 3.5
pain 0.40 0.41 0.07 -0.02 0.17 -0.11 0.11 -0.02 -0.14 0.42 0.09 0.33 0.07 0.70 0.298 5.0
pride 0.47 0.35 0.35 -0.12 0.03 -0.07 -0.02 0.39 -0.26 0.01 0.04 0.09 0.07 0.72 0.275 4.9
reasoning 0.39 0.40 0.25 0.47 -0.10 0.27 -0.01 -0.03 -0.21 -0.29 -0.06 0.04 0.02 0.81 0.188 5.7
remembering 0.32 0.25 0.14 0.10 0.12 0.42 -0.15 0.04 0.18 -0.06 -0.17 0.13 0.26 0.55 0.446 5.9
temperature 0.27 0.34 0.12 0.24 0.16 0.32 0.02 0.14 0.25 0.19 0.20 0.00 -0.13 0.57 0.429 7.8
tired 0.51 0.51 0.07 -0.13 0.04 0.04 0.00 -0.13 0.19 -0.01 -0.13 0.18 -0.09 0.66 0.342 3.1
MR1 MR3 MR5 MR6 MR4 MR7 MR2 MR8 MR10 MR9 MR12 MR11 MR13
SS loadings 5.00 2.56 1.12 0.91 0.83 0.80 0.73 0.66 0.60 0.56 0.34 0.26 0.24
Proportion Var 0.25 0.13 0.06 0.05 0.04 0.04 0.04 0.03 0.03 0.03 0.02 0.01 0.01
Cumulative Var 0.25 0.38 0.43 0.48 0.52 0.56 0.60 0.63 0.66 0.69 0.71 0.72 0.73
Proportion Explained 0.34 0.18 0.08 0.06 0.06 0.05 0.05 0.05 0.04 0.04 0.02 0.02 0.02
Cumulative Proportion 0.34 0.52 0.59 0.66 0.71 0.77 0.82 0.86 0.90 0.94 0.97 0.98 1.00
Mean item complexity = 4.5
Test of the hypothesis that 13 factors are sufficient.
The degrees of freedom for the null model are 190 and the objective function was 9.08 with Chi Square of 939.85
The degrees of freedom for the model are 8 and the objective function was 0.04
The root mean square of the residuals (RMSR) is 0.01
The df corrected root mean square of the residuals is 0.03
The harmonic number of observations is 110 with the empirical chi square 1.65 with prob < 0.99
The total number of observations was 112 with MLE Chi Square = 3.6 with prob < 0.89
Tucker Lewis Index of factoring reliability = 1.156
RMSEA index = 0 and the 90 % confidence intervals are NA 0.051
BIC = -34.15
Fit based upon off diagonal values = 1
Measures of factor score adequacy
MR1 MR3 MR5 MR6 MR4 MR7 MR2 MR8 MR10 MR9 MR12
Correlation of scores with factors 1.00 0.97 0.93 0.91 0.96 0.88 1.00 0.85 0.80 0.83 0.68
Multiple R square of scores with factors 1.00 0.95 0.87 0.82 0.91 0.78 0.99 0.73 0.64 0.70 0.46
Minimum correlation of possible factor scores 0.99 0.89 0.73 0.64 0.83 0.56 0.98 0.45 0.28 0.39 -0.08
MR11 MR13
Correlation of scores with factors 0.70 0.67
Multiple R square of scores with factors 0.48 0.45
Minimum correlation of possible factor scores -0.03 -0.10
Factor Analysis using method = minres
Call: fa(r = d4_all, nfactors = 13, rotate = "none", fm = "minres",
cor = chosenCorType)
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR3 MR5 MR6 MR4 MR7 MR2 MR8 MR10 MR9 MR12 MR11 MR13 h2 u2 com
angry 0.49 0.43 0.31 -0.19 -0.09 -0.17 0.12 -0.42 -0.06 -0.04 0.07 -0.09 0.13 0.83 0.172 5.0
choices 0.33 0.26 0.31 -0.01 -0.04 0.18 0.01 0.14 0.19 -0.02 0.18 -0.03 0.09 0.40 0.598 5.6
conscious 0.26 0.39 0.46 0.42 0.15 -0.25 -0.09 -0.03 -0.02 0.25 -0.08 -0.12 -0.14 0.80 0.199 5.7
depressed 0.46 0.30 0.33 -0.29 0.05 -0.25 0.09 -0.02 0.17 -0.34 0.00 0.16 -0.17 0.77 0.233 6.4
depth 0.29 0.30 0.22 0.25 0.06 0.06 0.03 -0.10 0.47 0.13 -0.12 0.00 0.15 0.58 0.420 4.6
disrespected 0.45 0.39 0.17 -0.04 0.05 -0.12 0.31 -0.03 -0.11 -0.06 0.06 -0.01 0.03 0.52 0.479 3.6
embarrassed 0.53 0.33 -0.27 0.03 0.67 -0.02 0.15 -0.04 -0.02 -0.05 0.00 -0.01 0.00 0.93 0.066 3.0
fear 0.86 -0.05 0.00 0.00 0.01 0.00 -0.51 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.005 1.6
guilt 0.36 0.32 0.17 0.12 0.10 0.25 -0.08 0.05 0.11 -0.16 0.40 -0.05 -0.05 0.56 0.435 5.4
happy 0.53 0.23 0.23 -0.24 0.27 -0.13 0.07 0.29 0.11 0.04 0.01 -0.15 0.17 0.69 0.312 4.7
hungry 0.64 0.45 0.04 -0.34 -0.05 0.36 0.05 -0.05 -0.07 0.12 -0.05 -0.07 -0.08 0.89 0.107 3.4
love 0.50 0.32 0.21 -0.20 0.15 -0.13 -0.03 0.41 0.01 -0.11 -0.13 -0.11 0.00 0.68 0.316 4.4
nauseated 0.86 -0.06 0.00 0.01 -0.02 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.005 1.6
odors 0.55 0.60 -0.30 0.06 -0.39 -0.10 -0.13 0.05 0.02 -0.01 0.01 -0.01 0.01 0.94 0.056 3.5
pain 0.40 0.41 0.07 -0.02 0.17 -0.11 0.11 -0.02 -0.14 0.42 0.09 0.33 0.07 0.70 0.298 5.0
pride 0.47 0.35 0.35 -0.12 0.03 -0.07 -0.02 0.39 -0.26 0.01 0.04 0.09 0.07 0.72 0.275 4.9
reasoning 0.39 0.40 0.25 0.47 -0.10 0.27 -0.01 -0.03 -0.21 -0.29 -0.06 0.04 0.02 0.81 0.188 5.7
remembering 0.32 0.25 0.14 0.10 0.12 0.42 -0.15 0.04 0.18 -0.06 -0.17 0.13 0.26 0.55 0.446 5.9
temperature 0.27 0.34 0.12 0.24 0.16 0.32 0.02 0.14 0.25 0.19 0.20 0.00 -0.13 0.57 0.429 7.8
tired 0.51 0.51 0.07 -0.13 0.04 0.04 0.00 -0.13 0.19 -0.01 -0.13 0.18 -0.09 0.66 0.342 3.1
MR1 MR3 MR5 MR6 MR4 MR7 MR2 MR8 MR10 MR9 MR12 MR11 MR13
SS loadings 5.00 2.56 1.12 0.91 0.83 0.80 0.73 0.66 0.60 0.56 0.34 0.26 0.24
Proportion Var 0.25 0.13 0.06 0.05 0.04 0.04 0.04 0.03 0.03 0.03 0.02 0.01 0.01
Cumulative Var 0.25 0.38 0.43 0.48 0.52 0.56 0.60 0.63 0.66 0.69 0.71 0.72 0.73
Proportion Explained 0.34 0.18 0.08 0.06 0.06 0.05 0.05 0.05 0.04 0.04 0.02 0.02 0.02
Cumulative Proportion 0.34 0.52 0.59 0.66 0.71 0.77 0.82 0.86 0.90 0.94 0.97 0.98 1.00
Mean item complexity = 4.5
Test of the hypothesis that 13 factors are sufficient.
The degrees of freedom for the null model are 190 and the objective function was 9.08 with Chi Square of 939.85
The degrees of freedom for the model are 8 and the objective function was 0.04
The root mean square of the residuals (RMSR) is 0.01
The df corrected root mean square of the residuals is 0.03
The harmonic number of observations is 110 with the empirical chi square 1.65 with prob < 0.99
The total number of observations was 112 with MLE Chi Square = 3.6 with prob < 0.89
Tucker Lewis Index of factoring reliability = 1.156
RMSEA index = 0 and the 90 % confidence intervals are NA 0.051
BIC = -34.15
Fit based upon off diagonal values = 1
Measures of factor score adequacy
MR1 MR3 MR5 MR6 MR4 MR7 MR2 MR8 MR10 MR9 MR12
Correlation of scores with factors 1.00 0.97 0.93 0.91 0.96 0.88 1.00 0.85 0.80 0.83 0.68
Multiple R square of scores with factors 1.00 0.95 0.87 0.82 0.91 0.78 0.99 0.73 0.64 0.70 0.46
Minimum correlation of possible factor scores 0.99 0.89 0.73 0.64 0.83 0.56 0.98 0.45 0.28 0.39 -0.08
MR11 MR13
Correlation of scores with factors 0.70 0.67
Multiple R square of scores with factors 0.48 0.45
Minimum correlation of possible factor scores -0.03 -0.10
[1] 3
[1] 3
Step 2: Run EFA with varimax rotation
Factor Analysis using method = minres
Call: fa(r = d4_all, nfactors = nfactors_d4_all, rotate = chosenRotType,
fm = "minres", cor = chosenCorType)
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR2 MR3 h2 u2 com
angry 0.69 0.15 0.22 0.55 0.45 1.3
choices 0.19 0.43 0.28 0.30 0.70 2.1
conscious 0.20 0.40 0.22 0.25 0.75 2.1
depressed 0.50 0.09 0.44 0.45 0.55 2.0
depth 0.19 0.51 0.10 0.31 0.69 1.4
disrespected 0.55 0.16 0.33 0.43 0.57 1.8
embarrassed 0.34 0.27 0.37 0.33 0.67 2.8
fear 0.40 0.30 0.32 0.35 0.65 2.8
guilt 0.21 0.53 0.19 0.36 0.64 1.6
happy 0.24 0.20 0.76 0.68 0.32 1.3
hungry 0.62 0.35 0.31 0.60 0.40 2.1
love 0.27 0.20 0.70 0.60 0.40 1.5
nauseated 0.54 0.17 0.37 0.46 0.54 2.0
odors 0.59 0.32 0.12 0.47 0.53 1.6
pain 0.42 0.26 0.26 0.31 0.69 2.5
pride 0.33 0.25 0.57 0.50 0.50 2.0
reasoning 0.35 0.53 0.03 0.40 0.60 1.7
remembering 0.14 0.54 0.13 0.33 0.67 1.3
temperature 0.05 0.68 0.14 0.49 0.51 1.1
tired 0.61 0.37 0.22 0.56 0.44 1.9
MR1 MR2 MR3
SS loadings 3.43 2.74 2.56
Proportion Var 0.17 0.14 0.13
Cumulative Var 0.17 0.31 0.44
Proportion Explained 0.39 0.31 0.29
Cumulative Proportion 0.39 0.71 1.00
Mean item complexity = 1.9
Test of the hypothesis that 3 factors are sufficient.
The degrees of freedom for the null model are 190 and the objective function was 9.08 with Chi Square of 939.85
The degrees of freedom for the model are 133 and the objective function was 1.84
The root mean square of the residuals (RMSR) is 0.06
The df corrected root mean square of the residuals is 0.07
The harmonic number of observations is 110 with the empirical chi square 127.91 with prob < 0.61
The total number of observations was 112 with MLE Chi Square = 186.58 with prob < 0.0015
Tucker Lewis Index of factoring reliability = 0.895
RMSEA index = 0.069 and the 90 % confidence intervals are 0.038 0.079
BIC = -440.98
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy
MR1 MR2 MR3
Correlation of scores with factors 0.86 0.85 0.86
Multiple R square of scores with factors 0.74 0.72 0.74
Minimum correlation of possible factor scores 0.48 0.43 0.48
back to TOC
Big factor loadings table for all studies (Studies 1-4)
Joining, by = "capacity"
Joining, by = "capacity"
Joining, by = "capacity"
Mean factor scores
Studies 1-2
Joining, by = c("study", "subid", "character", "age", "gender", "ethnicity", "trialNum", "bgColor", "capacity", "capWording", "hoverTime", "rt", "response", "responseNum", "age_group", "responseNumC")
joining factors with different levels, coercing to character vectorjoining factors with different levels, coercing to character vectorjoining factors with different levels, coercing to character vectorjoining factors with different levels, coercing to character vectorjoining factors with different levels, coercing to character vectorjoining factors with different levels, coercing to character vectorJoining, by = "subid"
Loading required package: Matrix
Attaching package: ‘Matrix’
The following object is masked from ‘package:tidyr’:
expand
Linear mixed model fit by REML ['lmerMod']
Formula: score ~ character * factor * age_group + (1 | subid)
Data: tempC
REML criterion at convergence: 86579.2
Scaled residuals:
Min 1Q Median 3Q Max
-4.3147 -0.6011 0.0312 0.6376 3.0275
Random effects:
Groups Name Variance Std.Dev.
subid (Intercept) 0.2319 0.4816
Residual 0.3482 0.5901
Number of obs: 47532, groups: subid, 400
Fixed effects:
Estimate Std. Error t value
(Intercept) -0.001266 0.024246 -0.05
characterrobot -0.249636 0.024246 -10.30
factorfactor1 0.007373 0.003830 1.93
factorfactor3 0.003199 0.003830 0.84
age_groupchildren 0.182400 0.024246 7.52
characterrobot:factorfactor1 0.270549 0.003830 70.64
characterrobot:factorfactor3 0.381627 0.003830 99.64
characterrobot:age_groupchildren 0.043430 0.024246 1.79
factorfactor1:age_groupchildren 0.458138 0.003830 119.62
factorfactor3:age_groupchildren -0.299420 0.003830 -78.18
characterrobot:factorfactor1:age_groupchildren -0.014001 0.003830 -3.66
characterrobot:factorfactor3:age_groupchildren -0.026621 0.003830 -6.95
Correlation of Fixed Effects:
(Intr) chrctr fctrf1 fctrf3 ag_grp chrc:1 chrc:3 chrc:_ fct1:_ fct3:_ ch:1:_
charactrrbt 0.010
factorfctr1 0.000 0.000
factorfctr3 0.000 0.000 -0.500
ag_grpchldr 0.001 0.030 0.000 0.000
chrctrrbt:1 0.000 0.000 0.013 -0.006 0.000
chrctrrbt:3 0.000 0.000 -0.006 0.013 0.000 -0.500
chrctrrbt:_ 0.030 0.001 0.000 0.000 0.010 0.000 0.000
fctrfctr1:_ 0.000 0.000 -0.002 0.001 0.000 0.033 -0.016 0.000
fctrfctr3:_ 0.000 0.000 0.001 -0.002 0.000 -0.016 0.033 0.000 -0.500
chrctrr:1:_ 0.000 0.000 0.033 -0.016 0.000 -0.002 0.001 0.000 0.013 -0.006
chrctrr:3:_ 0.000 0.000 -0.016 0.033 0.000 0.001 -0.002 0.000 -0.006 0.013 -0.500

Study 3

Studies 3-4

Factor scores by age
Study 1
Joining, by = "subid"

Study 2
Joining, by = "subid"

Studies 1-2
Joining, by = "subid"
Ignoring unknown aesthetics: y

Studies 3-4
Joining, by = c("age_group", "subid", "age", "character")
joining factors with different levels, coercing to character vectorJoining, by = "subid"

---
title: "Dimkid CogSci 2017 (Weisman, Dweck, & Markman, CogSci 2017)"
output:
  html_notebook:
    theme: flatly
    toc: yes
  html_document:
    toc: yes
  pdf_document:
    toc: yes
---

```{r global_options, include = FALSE}
knitr::opts_chunk$set(echo = FALSE, warning = FALSE, message = FALSE)
```

# Setup

```{r workspace setup}
# load libraries
library(tidyverse)
library(psych)
library(langcog) # source: https://github.com/langcog/langcog
library(RColorBrewer)
library(plotly)
library(lubridate)

# clear workspace
rm(list = ls(all = T))
graphics.off()
```

```{r functions}
# make na.rm = T versions of summary functions
mean_na <- function(x) {mean(x, na.rm = T)}
ci_lower_na <- function(x) {quantile(x, 0.025, na.rm = T)}
ci_upper_na <- function(x) {quantile(x, 0.975, na.rm = T)}

# make rounding function
round2 <- function(x) {format(round(x, 2), nsmall = 2)}

# make cleanup function
cleanup <- function(datasource, age_group) {
  if(grepl("adult", age_group)) {
    
    # set target dataset
    if(datasource == "study 1"){d <- d_raw_study1}
    if(datasource == "study 1b"){d <- d_raw_study1b}
    if(datasource == "study 1c"){d <- d_raw_study1c}
    
    # enact exclusionary criteria
    d_clean_1 <- d
    
    # recode background and demographic variables
    d_clean <- d_clean_1 %>%
      mutate( # deal with study number
        study = factor(study)) %>%
      mutate( # deal with race
        race_cat2 = factor(sub(" +$", "", ethnicity)),
        race_cat3 = factor(ifelse(grepl(" ", race_cat2) == T, "multiracial",
                                  as.character(race_cat2)))) %>%
      dplyr::select(study, subid:country_selfrep, age_group, race_cat3) %>%
      rename(race_cat = race_cat3) %>%
      mutate( # deal with religion (note: only dealing with childhood religion for now)
        religion_cat2 = factor(sub(" +$", "", religionChild)),
        religion_cat3 = factor(ifelse(grepl(" ", religion_cat2) == T, 
                                      "multireligious",
                                      as.character(religion_cat2)))) %>%
      dplyr::select(study:race_cat, religion_cat3) %>%
      rename(religion_cat = religion_cat3)
    
    # remove extraneous dfs and variables
    rm(d, d_clean_1)
  }
  
  if(grepl("child", age_group)) {
    
    # set target dataset
    if(datasource == "study 2"){d <- d_raw_study2}
    if(datasource == "study 3"){d <- d_raw_study3}
    if(datasource == "study 4"){d <- d_raw_study4}
    
    # recode background and demographic variables
    d_clean_2 <- d %>%
      mutate( # deal with study number
        study = factor(study),
        responseNum = ifelse(!is.na(responseNum), responseNum,
                             ifelse(response == "no", 0, 
                                    ifelse(response == "kinda", 0.5, 
                                           ifelse(response == "yes", 1, NA)))))
    # NOTE: need to reconcile race/ethnicity at some point...
    # NOTE: need to deal with gender at some point...
  
    d_clean <- d_clean_2
    
    # remove extraneous dfs and variables
    rm(d, d_clean_2)
  }
  
  # remove outliers if desired
  if(chosenOutlierHandling == "remove") {
    
    d_clean <- d_clean %>%
      gather(capacity, score, happy:pride) %>%
      group_by(character, capacity) %>%
      filter(!score %in% boxplot.stats(score, 2.5)$out) %>%
      spread(capacity, score) %>%
      arrange(character, subid)
    
  }
  
  # filter characters if desired
  if(is.element("none", chosenExclude)) {} else {
    
    d_clean <- d_clean %>%
      filter(!character %in% chosenExclude)
    
    }
    
  # filter items if desired
  if(is.element("none", chosenExcludeItem)) {} else {
    d_clean <- d_clean %>%
      dplyr::filter(!capacity %in% chosenExcludeItem)
  }
  
  # drop trials <250 ms
  d_clean <- d_clean %>%
    filter(rt >= 250 | is.na(rt))
  
  # center response variable
  if(datasource == "study 1b") {
    d_clean <- d_clean %>%
      mutate(responseNumC = responseNum - 4)
  } else {
    d_clean <- d_clean %>%
      mutate(responseNumC = responseNum - 0.5)
  }

    # rename character name variables
  if("charName" %in% names(d_clean)) {
    d_clean <- d_clean %>% rename(character = charName)
  }
  
  # cleanup
  d_clean <- d_clean %>%
    filter(!is.na(subid), !is.na(character), !is.na(capacity))
  
  # return cleaned dataset
  return(d_clean)
}

# make function for stripping dataframes for dimension reducation
makeDRDF <- function(datasource, chosenCondition) {
  
  # set target dataset
  if(datasource == "study 1"){d <- d1}
  if(datasource == "study 1b"){d <- d1b}
  if(datasource == "study 1c"){d <- d1c}
  if(datasource == "study 2"){d <- d2}
  if(datasource == "study 3"){d <- d3}
  if(datasource == "study 4"){d <- d4}

  # filter by character if specified
  if(chosenCondition %in% c("beetle", "robot")) {
    d <- d %>% filter(character == chosenCondition)
  }

  # make stripped dataframe for dimension reducation analyses
  d_strip <- d %>%
    filter(!is.na(character), !is.na(subid), !is.na(capacity), capacity != "") %>%
    mutate(subid = paste(character, subid, sep = "_")) %>%
    select(subid, capacity, responseNum) %>%
    spread(capacity, responseNum) %>%
    remove_rownames() %>%
    column_to_rownames(var = "subid")

  # return stripped dataframe
  return(d_strip)
}

# make demographics functions
demoSampleSize <- function(datasource) {

  # set target dataset
  if(datasource == "study 1"){d <- d1}
  if(datasource == "study 1b"){d <- d1b}
  if(datasource == "study 1c"){d <- d1c}
  if(datasource == "study 2"){d <- d2}
  if(datasource == "study 3"){d <- d3}
  if(datasource == "study 4"){d <- d4}

  # get distinct subids
  sample_size <- d %>% distinct(subid, character) %>% count(character) %>% data.frame()

  # add total sample size  
  sample_size <- rbind(sample_size %>% mutate(character = as.character(character)),
                       c(character = "all", n = d %>% distinct(subid) %>% count() %>% as.numeric()))
  
  # return dataframe
  return(sample_size)
}
demoDuration <- function(datasource) {

  # set target dataset
  if(datasource == "study 1"){d <- d1}
  if(datasource == "study 1b"){d <- d1b}
  if(datasource == "study 1c"){d <- d1c}
  if(datasource == "study 2"){d <- d2}
  if(datasource == "study 3"){d <- d3}
  if(datasource == "study 4"){d <- d4}

  # get sample size per character
  duration <- d %>%
    distinct(subid, character, duration) %>%
    mutate(duration = as.numeric(duration)) %>%
    group_by(character) %>%
    summarise(min_duration = min(duration, na.rm = T),
              max_duration = max(duration, na.rm = T),
              median_duration = median(duration, na.rm = T),
              mean_duration = mean(duration, na.rm = T),
              sd_duration = sd(duration, na.rm = T))

  # add total duration
  all <- d %>%
    distinct(subid, character, duration) %>%
    mutate(duration = as.numeric(duration)) %>%
    summarise(min_duration = min(duration, na.rm = T),
              max_duration = max(duration, na.rm = T),
              median_duration = median(duration, na.rm = T),
              mean_duration = mean(duration, na.rm = T),
              sd_duration = sd(duration, na.rm = T)) %>%
    mutate(character = "all")
  
  duration <- rbind(duration, all) # not sure why full_join doesn't work    

  # return dataframe
  return(duration)
}
demoAge <- function(datasource) {

  # set target dataset
  if(datasource == "study 1"){d <- d1}
  if(datasource == "study 1b"){d <- d1b}
  if(datasource == "study 1c"){d <- d1c}
  if(datasource == "study 2"){d <- d2}
  if(datasource == "study 3"){d <- d3}
  if(datasource == "study 4"){d <- d4}

  # get sample size per character
  age <- d %>%
    distinct(subid, character, age) %>%
    mutate(age = as.numeric(age)) %>%
    group_by(character) %>%
    summarise(min_age = min(age, na.rm = T),
              max_age = max(age, na.rm = T),
              median_age = median(age, na.rm = T),
              mean_age = mean(age, na.rm = T),
              sd_age = sd(age, na.rm = T))

  # add total age
  all <- d %>%
    distinct(subid, character, age) %>%
    mutate(age = as.numeric(age)) %>%
    summarise(min_age = min(age, na.rm = T),
              max_age = max(age, na.rm = T),
              median_age = median(age, na.rm = T),
              mean_age = mean(age, na.rm = T),
              sd_age = sd(age, na.rm = T)) %>%
    mutate(character = "all")
  age <- full_join(age, all)

  # return dataframe
  return(age)
}
demoGender <- function(datasource) {

  # set target dataset
  if(datasource == "study 1"){d <- d1}
  if(datasource == "study 1b"){d <- d1b}
  if(datasource == "study 1c"){d <- d1c}
  if(datasource == "study 2"){d <- d2}
  if(datasource == "study 3"){d <- d3}
  if(datasource == "study 4"){d <- d4}

  # get gender per character and overall
  gender <- data.frame(addmargins(with(d %>% distinct(subid, character, gender), 
                                       table(character, gender)))) %>%
    filter(gender != "Sum") %>%
    rename(n = Freq)
  
  gender <- gender %>%
    mutate(character = factor(ifelse(character == "Sum",
                                     "all", as.character(character)),
                              levels = c("beetle", "robot", "all"))) %>%
    arrange(character, gender) %>%
    spread(gender, n)
  
  # return dataframe
  return(gender)
}
demoRace <- function(datasource) {

  # set target dataset
  if(datasource == "study 1"){d <- d1}
  if(datasource == "study 1b"){d <- d1b}
  if(datasource == "study 1c"){d <- d1c}
  if(datasource == "study 2"){d <- d2}
  if(datasource == "study 3"){d <- d3}
  if(datasource == "study 4"){d <- d4}

  # get race per character and overall
  race <- data.frame(addmargins(with(d %>% distinct(subid, character, race_cat), 
                                     table(character, race_cat)))) %>%
    filter(race_cat != "Sum") %>%
    rename(n = Freq)

    race <- race %>%
      mutate(character = factor(ifelse(character == "Sum",
                                       "all", as.character(character)),
                                levels = c("beetle", "robot", "all"))) %>%
      arrange(character, race_cat) %>%
      spread(race_cat, n)
  
  # return dataframe
  return(race)
}

# plotting functions
makeFacetLabs <- function(df_plotting) {
  facet_labels <- array()
  df_plotting <- df_plotting %>% mutate(character = factor(character))
  for(i in 1:length(levels(df_plotting$character))) {
    df <- df_plotting %>% filter(character == levels(df_plotting$character)[i]) %>%
      select(character, n) %>% unique()
    facet_labels[i] <- paste0(df$character, " (n = ", df$n, ")")
  }
  names(facet_labels) <- levels(df_plotting$character)
  return(facet_labels)
}
```

```{r modeling decisions}
# remove outliers?
chosenOutlierHandling <- "keep"
# chosenOutlierHandling <- "remove"

# exclude any conditions (characters)?
chosenExclude <- "none"
# chosenExclude <- c("stapler", "car", "computer")

# exclude any items (mental capacities)?
# chosenExcludeItem <- "none"
# chosenExcludeItem <- "computations"
chosenExcludeItem <- c("metal", "on_off")

# NOTE: always choose minimal residual (fm = "minres") instead of ML because of non-normality

# for EFAs, what kind of correlation?
chosenCorType <- "cor" # pearson correlation
# chosenCorType <- "poly" # polychoric correlation

# for EFAs, what kind of rotation?
chosenRotType <- "varimax" # varimax rotation
# chosenRotType <- "oblimin" # oblimin rotation
# chosenRotType <- "none" # no rotation

data.frame("conditionsExcluded" = chosenExclude,
           "outlierHandling" = chosenOutlierHandling,
           "EFA_correlation" = chosenCorType,
           "EFA_rotation" = chosenRotType)
```

<p style="text-align:right"><a href="#header">back to TOC</a></p>

# Data preparation

```{r data upload}
# study 1 (2016-07-06, adults, 2 conditions, 3-point scale, "decide what to do" and "make plans")
d_raw_study1 <- read.csv("/Users/kweisman/Documents/Research (Stanford)/Projects/Dimkid/dimkid/data/adults/us_run-01_2016-06-05_anonymized.csv") %>%
  mutate(study = "study 1", age_group = "adults") %>% select(-X)

# study 1b (2017-07-19, adults, 2 conditions, 7-point scale, "decide what to do" and "make plans")
d_raw_study1b <- read.csv("/Users/kweisman/Documents/Research (Stanford)/Projects/Dimkid/dimkid/data/adults/us_run-02_2016-07-19_anonymized.csv") %>%
  mutate(study = "study 1b", age_group = "adults") %>% select(-X)

# study 1c (2016-12-08, adults, 2 conditions, 3-point scale, "have free will" and "have intentions")
d_raw_study1c <- read.csv("/Users/kweisman/Documents/Research (Stanford)/Projects/Dimkid/dimkid/data/adults/us_run-03_2016-12-08_anonymized.csv") %>%
  mutate(study = "study 1c", age_group = "adults") %>% select(-X)

# study 2 (June - December 2016, 7-9yo, 2 conditions, 3-point-scale, "decide what to do" and "make plans")
d_raw_study2 <- read.csv("/Users/kweisman/Documents/Research (Stanford)/Projects/Dimkid/dimkid/data/children/run-01_2017-07-24_anonymized.csv") %>%
  mutate(study = "study 2", age_group = "children_79") %>% select(-X)

# study 3 (January - June 2017, 7-9yo, 9 conditions, 3-point-scale, "decide what to do" and "make plans")
d_raw_study3 <- read.csv("/Users/kweisman/Documents/Research (Stanford)/Projects/Dimkid/dimkid/data/children/run-02_2017-08-03_anonymized.csv") %>%
  mutate(study = "study 3", age_group = "children_79") %>% select(-X) %>%
  mutate(dob = parse_datetime(dateOfBirth, "%m/%d/%y"),
         dot = parse_datetime(gsub("2017", "17", dateOfTest), "%m/%d/%y"), 
         age = interval(start = dob, end = dot) / duration(num = 1, units = "years")) %>%
  select(-dateOfBirth, -dateOfTest, -dob, -dot)

# study 4 (Mary 2017 - present, 4-6yo, 9 conditions, 3-point-scale, "decide what to do" and "make plans")
d_raw_study4 <- read.csv("/Users/kweisman/Documents/Research (Stanford)/Projects/Dimkid/dimkid/data/children/run-03_2017-08-03_anonymized.csv") %>%
  mutate(study = "study 4", age_group = "children_46") %>% select(-X) %>%
  mutate(dob = parse_datetime(dateOfBirth, "%m/%d/%y"),
         dot = parse_datetime(gsub("2017", "17", dateOfTest), "%m/%d/%y"), 
         age = interval(start = dob, end = dot) / duration(num = 1, units = "years")) %>%
  select(-dateOfBirth, -dateOfTest, -dob, -dot)
```

```{r data cleanup}
# clean up datasets
d1 <- cleanup("study 1", "adults")
d1b <- cleanup("study 1", "adults")
d1c <- cleanup("study 1", "adults")
d2 <- cleanup("study 2", "children")
d3 <- cleanup("study 3", "children")
d4 <- cleanup("study 4", "children")

# tweak by hand
d2 <- d2 %>%
  filter(!is.na(age)) %>%
  filter(age >= 7, age < 10) %>%
  filter(character != "elephant")

d3 <- d3 %>%
  filter(!is.na(character), character != "")

d4 <- d4 %>%
  filter(!is.na(character), character != "")
```

```{r dataframes for dimension reducation}
# make dataframes for s1
# d1_beetle <- makeDRDF("study 1", "beetle")
# d1_robot <- makeDRDF("study 1", "robot")
d1_all <- makeDRDF("study 1", "all")

# make dataframes for follow-up studies to s1
d1b_all <- makeDRDF("study 1b", "all")
d1c_all <- makeDRDF("study 1c", "all")

# make dataframes for study 2
# d2_beetle <- makeDRDF("study 2", "beetle")
# d2_robot <- makeDRDF("study 2", "robot")
d2_all <- makeDRDF("study 2", "all")

# make dataframes for study 3
# d3_beetle <- makeDRDF("study 3", "beetle")
# d3_robot <- makeDRDF("study 3", "robot")
d3_all <- makeDRDF("study 3", "all")

# make dataframes for study 4
d4_all <- makeDRDF("study 4", "all")
```

<p style="text-align:right"><a href="#header">back to TOC</a></p>

# Analysis plan

For all studies we conduct exploratory factor analyses using Pearson correlations to find minimum residual solutions. 

For each study, we first examine maximal unrotated and rotated solutions. To determine the maximum number of factors to extract, we use the following rule of thumb: With $p$ observations per participant, we can extract a maximum of $k$ factors, where $(p-k)*2 > p+k$, i.e., $k < p/3$. Thus, with 40 mental capacity items, we can extract a maximum of 13 factors.

To determine how many factors to retain, we use the following preset retention criteria, considering the unrotated maximal solution (unless otherwise noted):

  - Each factor must have an eigenvalue >1.0.
  - Each factor must individually account for >5% of the total variance in the maximal model.
  - After rotation, each factor must be the dominant factor (i.e., the factor with the highest factor loading) for ≥1 mental capacity item.

We then examine and interpret varimax-rotated solutions, extracting only the number of factors that meet these criteria.

# Study 1

Study information:

* Design: 2 conditions (beetle, robot), 3-point response scale, "decide what to do" and "have intentions"
* Population: adults
* Date conducted: 2016-07-06 (MTurk)

## Demographics

```{r s1 demographics}
# make demographics tables
demoSampleSize("study 1")
demoDuration("study 1")
demoAge("study 1")
demoGender("study 1")
demoRace("study 1")
```

<p style="text-align:right"><a href="#header">back to TOC</a></p>

## Exploratory factor analysis

### Step 1: Run maximal EFA (without and with rotation)

```{r s1 all no rotation}
# examine scree plot
fa.parallel(d1_all)

# run EFA without rotation with N factors
efa_d1_all_unrotated <- fa(d1_all, 13, rotate = "none",
                           cor = chosenCorType, fm = "minres")
print(efa_d1_all_unrotated)

# examine eigenvalues and variance explained
efa_d1_all_unrotated_eigenvalues <- print(efa_d1_all_unrotated)$Vaccounted %>%
  t() %>%
  data.frame()

# count factors with eigenvalues > 1 and variance explained > 5%
efa_d1_all_unrotated_nfactors <- efa_d1_all_unrotated_eigenvalues %>%
  filter(SS.loadings > 1, Proportion.Explained > 0.05) %>%
  count() %>%
  as.numeric()
efa_d1_all_unrotated_nfactors
```

```{r s1 all rotation}
efa_d1_all_rotated_max <- fa(d1_all, 13, rotate = chosenRotType,
                           cor = chosenCorType, fm = "minres")

efa_d1_all_rotated <- fa(d1_all, efa_d1_all_unrotated_nfactors, rotate = chosenRotType,
                           cor = chosenCorType, fm = "minres")

# check that each of these factors is the dominant factor for at least one mental capacity item
efa_d1_all_rotated_loadings <- fa.sort(loadings(efa_d1_all_rotated)[]) %>%
  data.frame() %>%
  rownames_to_column("capacity") %>%
  gather(factor, loading, -capacity) %>%
  mutate(loading_abs = abs(loading)) %>%
  group_by(capacity) %>%
  top_n(1, loading_abs) %>%
  ungroup()
efa_d1_all_rotated_loadings

# drop any factors where n < 1
efa_d1_all_rotated_loadings %>% 
  count(factor) %>% 
  filter(n > 0)

# set number of factors to extract
nfactors_d1_all <- efa_d1_all_rotated_loadings %>% 
  count(factor) %>% 
  filter(n > 0) %>%
  nrow()
nfactors_d1_all
```

### Step 2: Run EFA with varimax rotation

```{r s1 all varimax rotation}
# run EFA with rotation with N factors
efa_d1_all_rotatedN <- fa(d1_all, nfactors_d1_all, 
                          rotate = chosenRotType, cor = chosenCorType, fm = "minres")
print(efa_d1_all_rotatedN)

# get loadings for each factor
efa_d1_all_rotatedN_loadings <- loadings(efa_d1_all_rotatedN)[] %>%
  data.frame() %>% 
  rownames_to_column(var = "capacity")
```

<p style="text-align:right"><a href="#header">back to TOC</a></p>

#### Factor loadings table

```{r s1 loadings table}
data.frame(loadings(fa.sort(efa_d1_all_rotatedN))[]) %>%
  rownames_to_column("capacity") %>%
  mutate_at(vars(starts_with("M")), funs(round2))
```

# Study 2

Study information:

* Design: 2 conditions (beetle, robot), 3-point response scale, "decide what to do" and "have intentions"
* Population: 7-9yo children
* Date conducted: June - December 2016

## Demographics

```{r s2 demographics}
# make demographics tables
demoSampleSize("study 2")
# demoDuration("study 2")
demoAge("study 2")
demoGender("study 2")
# demoRace("study 2")
```

<p style="text-align:right"><a href="#header">back to TOC</a></p>

## Exploratory factor analysis

### Step 1: Run maximal EFA (without and with rotation)

```{r s2 all no rotation}
# examine scree plot
fa.parallel(d2_all)

# run EFA without rotation with N factors
efa_d2_all_unrotated <- fa(d2_all, 13, rotate = "none",
                           cor = chosenCorType, fm = "minres")
print(efa_d2_all_unrotated)

# examine eigenvalues and variance explained
efa_d2_all_unrotated_eigenvalues <- print(efa_d2_all_unrotated)$Vaccounted %>%
  t() %>%
  data.frame()

# count factors with eigenvalues > 1 and variance explained > 5%
efa_d2_all_unrotated_nfactors <- efa_d2_all_unrotated_eigenvalues %>%
  filter(SS.loadings > 1, Proportion.Explained > 0.05) %>%
  count() %>%
  as.numeric()
efa_d2_all_unrotated_nfactors
```

```{r s2 all rotation}
efa_d2_all_rotated_max <- fa(d2_all, 13, rotate = chosenRotType,
                           cor = chosenCorType, fm = "minres")

efa_d2_all_rotated <- fa(d2_all, efa_d2_all_unrotated_nfactors, rotate = chosenRotType,
                           cor = chosenCorType, fm = "minres")

# check that each of these factors is the dominant factor for at least one mental capacity item
efa_d2_all_rotated_loadings <- fa.sort(loadings(efa_d2_all_rotated)[]) %>%
  data.frame() %>%
  rownames_to_column("capacity") %>%
  gather(factor, loading, -capacity) %>%
  mutate(loading_abs = abs(loading)) %>%
  group_by(capacity) %>%
  top_n(1, loading_abs) %>%
  ungroup()
efa_d2_all_rotated_loadings

# drop any factors where n < 1
efa_d2_all_rotated_loadings %>% 
  count(factor) %>% 
  filter(n > 0)

# set number of factors to extract
nfactors_d2_all <- efa_d2_all_rotated_loadings %>% 
  count(factor) %>% 
  filter(n > 0) %>%
  nrow()
nfactors_d2_all
```

### Step 2: Run EFA with varimax rotation

```{r s2 all varimax rotation}
# run EFA with rotation with N factors
efa_d2_all_rotatedN <- fa(d2_all, nfactors_d2_all, 
                          rotate = chosenRotType, cor = chosenCorType, fm = "minres")
print(efa_d2_all_rotatedN)

# get loadings for each factor
efa_d2_all_rotatedN_loadings <- loadings(efa_d2_all_rotatedN)[] %>%
  data.frame() %>% 
  rownames_to_column(var = "capacity")
```

<p style="text-align:right"><a href="#header">back to TOC</a></p>

#### Factor loadings table

```{r s2 loadings table}
data.frame(loadings(fa.sort(efa_d2_all_rotatedN))[]) %>%
  rownames_to_column("capacity") %>%
  mutate_at(vars(starts_with("M")), funs(round2))
```

# Study 3 

Study information:

* Design: 7 conditions (beetle, robot, ...) + 2 follow-up conditions, 3-point response scale, "decide what to do" and "have intentions"
* Population: 7-9yo children
* Date conducted: January - June 2017

## Demographics

```{r s3 demographics}
# make demographics tables
demoSampleSize("study 3")
# demoDuration("study 3")
# demoAge("study 3")
# demoGender("study 3")
# demoRace("study 3")
```

<p style="text-align:right"><a href="#header">back to TOC</a></p>

## Exploratory factor analysis

### Step 1: Run maximal EFA (without and with rotation)

```{r s3 all no rotation}
# examine scree plot
fa.parallel(d3_all)

# run EFA without rotation with N factors
efa_d3_all_unrotated <- fa(d3_all, 13, rotate = "none",
                           cor = chosenCorType, fm = "minres")
print(efa_d3_all_unrotated)

# examine eigenvalues and variance explained
efa_d3_all_unrotated_eigenvalues <- print(efa_d3_all_unrotated)$Vaccounted %>%
  t() %>%
  data.frame()

# count factors with eigenvalues > 1 and variance explained > 5%
efa_d3_all_unrotated_nfactors <- efa_d3_all_unrotated_eigenvalues %>%
  filter(SS.loadings > 1, Proportion.Explained > 0.05) %>%
  count() %>%
  as.numeric()
efa_d3_all_unrotated_nfactors
```

```{r s3 all rotation}
efa_d3_all_rotated_max <- fa(d3_all, 13, rotate = chosenRotType,
                           cor = chosenCorType, fm = "minres")

efa_d3_all_rotated <- fa(d3_all, efa_d3_all_unrotated_nfactors, rotate = chosenRotType,
                           cor = chosenCorType, fm = "minres")

# check that each of these factors is the dominant factor for at least one mental capacity item
efa_d3_all_rotated_loadings <- fa.sort(loadings(efa_d3_all_rotated)[]) %>%
  data.frame() %>%
  rownames_to_column("capacity") %>%
  gather(factor, loading, -capacity) %>%
  mutate(loading_abs = abs(loading)) %>%
  group_by(capacity) %>%
  top_n(1, loading_abs) %>%
  ungroup()
efa_d3_all_rotated_loadings

# drop any factors where n < 1
efa_d3_all_rotated_loadings %>% 
  count(factor) %>% 
  filter(n > 0)

# set number of factors to extract
nfactors_d3_all <- efa_d3_all_rotated_loadings %>% 
  count(factor) %>% 
  filter(n > 0) %>%
  nrow()
nfactors_d3_all
```

### Step 2: Run EFA with varimax rotation

```{r s3 all varimax rotation}
# run EFA with rotation with N factors
efa_d3_all_rotatedN <- fa(d3_all, nfactors_d3_all, 
                          rotate = chosenRotType, cor = chosenCorType, fm = "minres")
print(efa_d3_all_rotatedN)

# get loadings for each factor
efa_d3_all_rotatedN_loadings <- loadings(efa_d3_all_rotatedN)[] %>%
  data.frame() %>% 
  rownames_to_column(var = "capacity")
```

<p style="text-align:right"><a href="#header">back to TOC</a></p>

#### Factor loadings table

```{r s3 loadings table}
data.frame(loadings(fa.sort(efa_d3_all_rotatedN))[]) %>%
  rownames_to_column("capacity") %>%
  mutate_at(vars(starts_with("M")), funs(round2))
```

### Subscales

#### Reliability (and intercorrelations - see alpha)

```{r s3 subscale reliability}
# Cronbach's alpha (subscales)
keys.list <- list(SOUL = c("pride", "depressed", "disrespected", "guilt", 
                           "embarrassed", "happy", "love"),
                  BODY = c("hungry", "odors", "fear", "pain", "tired", "angry", "nauseated"),
                  MIND = c("reasoning", "choices", "remembering", "temperature", 
                           "conscious", "depth")) 
scores <- scoreItems(keys.list, d3_all, min = 0, max = 1)  # or just use the keys.lit
# summary(scores)
scores

# omega
omega(d3_all, plot = F)
```

# Study 4

Study information:

* Design: 7 conditions (beetle, robot, ...) + 2 follow-up conditions (doll, teddy bear), 3-point response scale, "decide what to do" and "have intentions"
* Population: 4-6yo children
* Date conducted: March 2017 - present

## Demographics

```{r s4 demographics}
# make demographics tables
demoSampleSize("study 4")
# demoDuration("study 4")
demoAge("study 4")
# demoGender("study 4")
# demoRace("study 4")
```

<p style="text-align:right"><a href="#header">back to TOC</a></p>

## Exploratory factor analysis

### Step 1: Run maximal EFA (without and with rotation)

```{r s4 all no rotation}
# examine scree plot
fa.parallel(d4_all)

# run EFA without rotation with N factors
efa_d4_all_unrotated <- fa(d4_all, 13, rotate = "none",
                           cor = chosenCorType, fm = "minres")
print(efa_d4_all_unrotated)

# examine eigenvalues and variance explained
efa_d4_all_unrotated_eigenvalues <- print(efa_d4_all_unrotated)$Vaccounted %>%
  t() %>%
  data.frame()

# count factors with eigenvalues > 1 and variance explained > 5%
efa_d4_all_unrotated_nfactors <- efa_d4_all_unrotated_eigenvalues %>%
  filter(SS.loadings > 1, Proportion.Explained > 0.05) %>%
  count() %>%
  as.numeric()
efa_d4_all_unrotated_nfactors
```

```{r s4 all rotation}
efa_d4_all_rotated_max <- fa(d4_all, 13, rotate = chosenRotType,
                           cor = chosenCorType, fm = "minres")

efa_d4_all_rotated <- fa(d4_all, efa_d4_all_unrotated_nfactors, rotate = chosenRotType,
                           cor = chosenCorType, fm = "minres")

# check that each of these factors is the dominant factor for at least one mental capacity item
efa_d4_all_rotated_loadings <- fa.sort(loadings(efa_d4_all_rotated)[]) %>%
  data.frame() %>%
  rownames_to_column("capacity") %>%
  gather(factor, loading, -capacity) %>%
  mutate(loading_abs = abs(loading)) %>%
  group_by(capacity) %>%
  top_n(1, loading_abs) %>%
  ungroup()
efa_d4_all_rotated_loadings

# drop any factors where n < 1
efa_d4_all_rotated_loadings %>% 
  count(factor) %>% 
  filter(n > 0)

# set number of factors to extract
nfactors_d4_all <- efa_d4_all_rotated_loadings %>% 
  count(factor) %>% 
  filter(n > 0) %>%
  nrow()
nfactors_d4_all
```

### Step 2: Run EFA with varimax rotation

```{r s4 all varimax rotation}
# run EFA with rotation with N factors
efa_d4_all_rotatedN <- fa(d4_all, nfactors_d4_all, 
                          rotate = chosenRotType, cor = chosenCorType, fm = "minres")
print(efa_d4_all_rotatedN)

# get loadings for each factor
efa_d4_all_rotatedN_loadings <- loadings(efa_d4_all_rotatedN)[] %>%
  data.frame() %>% 
  rownames_to_column(var = "capacity")
```

<p style="text-align:right"><a href="#header">back to TOC</a></p>

#### Factor loadings table

```{r s4 loadings table}
data.frame(loadings(fa.sort(efa_d4_all_rotatedN))[]) %>%
  rownames_to_column("capacity") %>%
  mutate_at(vars(starts_with("M")), funs(round2))
```

# Big factor loadings table for all studies (Studies 1-4)

```{r all studies loadings table}
# manually set 3 factors
order_s1_manual <- loadings(fa.sort(fa(d1_all, nfactors = 3,
                                       rotate = chosenRotType, cor = chosenCorType)))[] %>%
  data.frame() %>%
  rownames_to_column(var = "capacity") %>%
  rownames_to_column(var = "order1_manual") %>%
  rename(s1_heart = MR2, s1_body = MR1, s1_mind = MR3)

order_s1 <- loadings(fa.sort(efa_d1_all_rotatedN))[] %>%
  data.frame() %>%
  rownames_to_column(var = "capacity") %>%
  rownames_to_column(var = "order1") %>%
  rename(s1_heart = MR2, s1_body = MR1, s1_mind = MR3)

order_s2 <- loadings(fa.sort(efa_d2_all_rotatedN))[] %>%
  data.frame() %>%
  rownames_to_column(var = "capacity") %>%
  rename(s2_body = MR2, s2_heart = MR1, s2_mind = MR3)

order_s3 <- loadings(fa.sort(efa_d3_all_rotatedN))[] %>%
  data.frame() %>%
  rownames_to_column(var = "capacity") %>%
  rename(s3_body = MR1, s3_heart = MR2, s3_mind = MR3)

order_s4 <- loadings(fa.sort(efa_d4_all_rotatedN))[] %>%
  data.frame() %>%
  rownames_to_column(var = "capacity") %>%
  rename(s4_body = MR1, s4_heart = MR3, s4_mind = MR2)

bigTable <- order_s1_manual %>% # could substitute order_s1
  full_join(order_s2) %>%
  full_join(order_s3) %>%
  full_join(order_s4) %>%
  mutate_at(vars(starts_with("s")), funs(round2)) %>%
  select(order1_manual, # could subistitute order_s1
         capacity, ends_with("heart"), ends_with("body"), ends_with("mind")) 

bigTable
```

# Figures

```{r plotting setup character means, include = F}
# bootstrap 95% CIs for ratings by character (nonparametric)
# study 1
char_plotting_ratings_s1 <- d1 %>% 
  select(subid, character, capacity, responseNum) %>%
  multi_boot(column = "responseNum",
             summary_function = "mean_na",
             summary_groups = c("character", "capacity"),
             statistics_functions = c("ci_lower_na", "mean_na", "ci_upper_na")) %>%
  full_join(demoSampleSize("study 1") %>% filter(character != "all")) %>%
  mutate(study = "study 1")

# study 2
char_plotting_ratings_s2 <- d2 %>% 
  select(subid, character, capacity, responseNum) %>%
  multi_boot(column = "responseNum",
             summary_function = "mean_na",
             summary_groups = c("character", "capacity"),
             statistics_functions = c("ci_lower_na", "mean_na", "ci_upper_na")) %>%
  full_join(demoSampleSize("study 2") %>% filter(character != "all")) %>%
  mutate(study = "study 2")

# study 3
char_plotting_ratings_s3 <- d3 %>% 
  select(subid, character, capacity, responseNum) %>%
  multi_boot(column = "responseNum",
             summary_function = "mean_na",
             summary_groups = c("character", "capacity"),
             statistics_functions = c("ci_lower_na", "mean_na", "ci_upper_na")) %>%
  full_join(demoSampleSize("study 3") %>% filter(character != "all")) %>%
  mutate(study = "study 3")

# study 4
char_plotting_ratings_s4 <- d4 %>% 
  select(subid, character, capacity, responseNum) %>%
  multi_boot(column = "responseNum",
             summary_function = "mean_na",
             summary_groups = c("character", "capacity"),
             statistics_functions = c("ci_lower_na", "mean_na", "ci_upper_na")) %>%
  full_join(demoSampleSize("study 4") %>% filter(character != "all")) %>%
  mutate(study = "study 4")
```

```{r plotting setup character means merge, include = F}
char_plotting_ratings_all <- char_plotting_ratings_s1 %>%
  full_join(char_plotting_ratings_s2) %>%
  full_join(char_plotting_ratings_s3) %>%
  full_join(char_plotting_ratings_s4) %>%
  filter(!is.na(character)) %>%
  ungroup() %>%
  mutate(study = factor(study),
         condition = factor(character,
                            levels = c("computer", "doll", "teddy_bear", "robot", 
                                       "beetle", "bird", "mouse", "goat", "elephant")))
```

```{r plotting setup capacity wordings, include = F}
char_plotting_wordings <- char_plotting_ratings_all %>%
  ungroup() %>%
  select(capacity) %>%
  distinct() %>% 
  mutate(wording = factor(
    recode(capacity,
           happy = "feel happy",
           depressed = "feel sad",
           fear = "feel scared",
           angry = "get angry",
           calm = "feel calm",
           sounds = "hear sounds",
           seeing = "see things",
           temperature = "sense temperatures",
           odors = "smell things",
           depth = "sense... close by or far away",
           computations = "do math",
           thoughts = "have thoughts",
           reasoning = "figure out how to do things",
           remembering = "remember things",
           beliefs = "have beliefs...",
           hungry = "get hungry",
           tired = "feel tired",
           pain = "feel pain",
           nauseated = "feel sick...",
           safe = "feel safe",
           love = "feel love",
           recognizing = "recognize somebody else",
           communicating = "communicate with somebody else",
           guilt = "feel guilty",
           disrespected = "get hurt feelings",
           free_will = "decide what to do",
           choices = "make choices",
           self_restraint = "have self-control...",
           intentions = "make plans",
           goal = "have goals...",
           conscious = "be aware of things",
           self_aware = "be aware of itself",
           desires = "have desires...",
           embarrassed = "feel embarrassed",
           emo_recog = "understand how somebody else is feeling",
           joy = "feel joy",
           morality = "know what's nice and what's mean",
           personality = "have a personality...",
           pleasure = "feel pleasure...",
           proud = "feel proud")))
```

```{r plotting setup loadings, include = F}
# merge with loadings, orderings, and dominant factors from each study 
char_plotting <- char_plotting_ratings_all %>%
  full_join(char_plotting_wordings) %>%
  full_join(order_s1 %>%
              rename(s1_MR1 = s1_body, s1_MR2 = s1_heart, s1_MR3 = s1_mind) %>%
              mutate(s1_MR1_abs = abs(s1_MR1),
                     s1_MR2_abs = abs(s1_MR2),
                     s1_MR3_abs = abs(s1_MR3),
                     s1_factor = 
                       ifelse(s1_MR1_abs > s1_MR2_abs &
                                s1_MR1_abs > s1_MR3_abs, "BODY",
                              ifelse(s1_MR2_abs > s1_MR1_abs &
                                       s1_MR2_abs > s1_MR3_abs, "HEART",
                                     ifelse(s1_MR3_abs > s1_MR1_abs &
                                              s1_MR3_abs > s1_MR2_abs, "MIND",
                                            NA))),
                     s1_color = recode(s1_factor,
                                       "BODY" = "#E41A1C",
                                       "HEART" = "#377EB8",
                                       "MIND" = "#4DAF4A"),
                     s1_order = as.numeric(order1)) %>%
              select(-s1_MR1_abs, -s1_MR2_abs, -s1_MR3_abs)) %>%
  full_join(order_s2 %>%
              data.frame() %>%
              rename(s2_MR1 = s2_heart, s2_MR2 = s2_body, s2_MR3 = s2_mind) %>%
              mutate(s2_MR1_abs = abs(s2_MR1),
                     s2_MR2_abs = abs(s2_MR2),
                     s2_MR3_abs = abs(s2_MR3),
                     s2_factor = 
                       ifelse(s2_MR1_abs > s2_MR2_abs &
                                s2_MR1_abs > s2_MR3_abs, "BODY",
                              ifelse(s2_MR2_abs > s2_MR1_abs &
                                       s2_MR2_abs > s2_MR3_abs, "HEART",
                                     ifelse(s2_MR3_abs > s2_MR1_abs &
                                              s2_MR3_abs > s2_MR2_abs, "MIND",
                                            NA))),
                     s2_color = recode(s2_factor,
                                       "BODY" = "#E41A1C",
                                       "HEART" = "#377EB8",
                                       "MIND" = "#4DAF4A")) %>%
              rownames_to_column(var = "s2_order") %>%
              mutate(s2_order = as.numeric(s2_order)) %>%
              select(-s2_MR1_abs, -s2_MR2_abs, -s2_MR3_abs)) %>%
  full_join(order_s3 %>%
              rename(s3_MR1 = s3_heart, s3_MR2 = s3_body, s3_MR3 = s3_mind) %>%
              mutate(s3_MR1_abs = abs(s3_MR1),
                     s3_MR2_abs = abs(s3_MR2),
                     s3_MR3_abs = abs(s3_MR3),
                     s3_factor = 
                       ifelse(s3_MR1_abs > s3_MR2_abs &
                                s3_MR1_abs > s3_MR3_abs, "BODY",
                              ifelse(s3_MR2_abs > s3_MR1_abs &
                                       s3_MR2_abs > s3_MR3_abs, "HEART",
                                     ifelse(s3_MR3_abs > s3_MR1_abs &
                                              s3_MR3_abs > s3_MR2_abs, "MIND",
                                            NA))),
                     s3_color = recode(s3_factor,
                                       "BODY" = "#E41A1C",
                                       "HEART" = "#377EB8",
                                       "MIND" = "#4DAF4A")) %>%
              rownames_to_column(var = "s3_order") %>%
              mutate(s3_order = as.numeric(s3_order)) %>%
              select(-s3_MR1_abs, -s3_MR2_abs, -s3_MR3_abs)) %>%
  full_join(order_s4 %>%
              rename(s4_MR1 = s4_body, s4_MR2 = s4_mind, s4_MR3 = s4_heart) %>%
              mutate(s4_MR1_abs = abs(s4_MR1),
                     s4_MR2_abs = abs(s4_MR2),
                     s4_MR3_abs = abs(s4_MR3),
                     s4_factor = 
                       ifelse(s4_MR1_abs > s4_MR2_abs &
                                s4_MR1_abs > s4_MR3_abs, "BODY",
                              ifelse(s4_MR2_abs > s4_MR1_abs &
                                       s4_MR2_abs > s4_MR3_abs, "HEART",
                                     ifelse(s4_MR3_abs > s4_MR1_abs &
                                              s4_MR3_abs > s4_MR2_abs, "MIND",
                                            NA))),
                     s4_color = recode(s4_factor,
                                       "BODY" = "#E41A1C",
                                       "HEART" = "#377EB8",
                                       "MIND" = "#4DAF4A")) %>%
              rownames_to_column(var = "s4_order") %>%
              mutate(s4_order = as.numeric(s4_order)) %>%
              select(-s4_MR1_abs, -s4_MR2_abs, -s4_MR3_abs))

# configure plot labels
label_df_s1 <- char_plotting %>% filter(study == "study 1") %>% select(condition, n) %>% unique()
label_df_s2 <- char_plotting %>% filter(study == "study 2") %>% select(condition, n) %>% unique()
label_df_s3 <- char_plotting %>% filter(study == "study 3") %>% select(condition, n) %>% unique()
label_df_s4 <- char_plotting %>% filter(study == "study 4") %>% select(condition, n) %>% unique()

facetLabs_s1 <- gsub(" \\(", "\n(", makeFacetLabs(char_plotting %>% filter(study == "study 1")))
facetLabs_s2 <- gsub(" \\(", "\n(", makeFacetLabs(char_plotting %>% filter(study == "study 2")))
facetLabs_s3 <- gsub(" \\(", "\n(", makeFacetLabs(char_plotting %>% filter(study == "study 3")))
facetLabs_s4 <- gsub(" \\(", "\n(", makeFacetLabs(char_plotting %>% filter(study == "study 4")))

# configure custom palette
myPalette <- brewer.pal(3, "Set1"); names(myPalette) <- c("BODY", "HEART", "MIND")

palette_base <- char_plotting %>% 
  select(capacity, ends_with("_factor")) %>%
  distinct()
# adjust by hand depending on order of factors!!
palette_s1 <- c(rep(myPalette["MIND"], palette_base %>% filter(s1_factor == "MIND") %>% count()),
                rep(myPalette["HEART"], palette_base %>% filter(s1_factor == "HEART") %>% count()),
                rep(myPalette["BODY"], palette_base %>% filter(s1_factor == "BODY") %>% count()))
palette_s2 <- c(rep(myPalette["MIND"], palette_base %>% filter(s2_factor == "MIND") %>% count()),
                rep(myPalette["BODY"], palette_base %>% filter(s2_factor == "BODY") %>% count()),
                rep(myPalette["HEART"], palette_base %>% filter(s2_factor == "HEART") %>% count()))
palette_s3 <- c(rep(myPalette["MIND"], palette_base %>% filter(s3_factor == "MIND") %>% count()),
                rep(myPalette["BODY"], palette_base %>% filter(s3_factor == "BODY") %>% count()),
                rep(myPalette["HEART"], palette_base %>% filter(s3_factor == "HEART") %>% count()))
# palette_s4 <- c(rep(myPalette["MIND"], palette_base %>% filter(s4_factor == "MIND") %>% count()),
#                 rep(myPalette["HEART"], palette_base %>% filter(s4_factor == "HEART") %>% count()),
#                 rep(myPalette["BODY"], palette_base %>% filter(s4_factor == "BODY") %>% count()))
```

## 3D scatterplots

Factor loadings for the 40 mental capacities on the three rotated factors in Study 1. Items are colored by their dominant factor loading: Items that loaded most strongly on the body factor (bodily states and will) are in red; items that loaded most strongly on the heart factor (social-emotional experiences and morality) are in blue; and items that loaded most strongly on the mind factor (perceptual-cognitive abilities and goal pursuit) are in green.

### Study 1 (adults)

```{r figure 3d scatter s1}
# set up labels for plot (shortened version of mental capacity items)
wording_s1 <- loadings(efa_d1_all_rotatedN)[] %>%
  data.frame() %>%
  rownames_to_column(var = "item") %>%
  select(item) %>%
  mutate(wording = factor(
    recode(item,
           happy = "feel happy",
           depressed = "feel sad",
           fear = "feel scared",
           angry = "get angry",
           calm = "feel calm",
           sounds = "hear sounds",
           seeing = "see things",
           temperature = "sense temperatures",
           odors = "smell things",
           depth = "sense whether something is close by or far away",
           computations = "do math",
           thoughts = "have thoughts",
           reasoning = "figure out how to do things",
           remembering = "remember things",
           beliefs = "have beliefs, like when you think something is true",
           hungry = "get hungry",
           tired = "feel tired",
           pain = "feel pain",
           nauseated = "feel sick, like when you feel like you might throw up",
           safe = "feel safe",
           love = "feel love",
           recognizing = "recognize somebody else",
           communicating = "communicate with somebody else",
           guilt = "feel guilty",
           disrespected = "get hurt feelings",
           free_will = "decide what to do",
           choices = "make choices",
           self_restraint = "have self-control, like when you stop yourself from doing something you shouldn't do",
           intentions = "make plans",
           goal = "have goals, like when you're working hard to do something or make something happen",
           conscious = "be aware of things",
           self_aware = "be aware of itself",
           desires = "have desires, like when you really want something",
           embarrassed = "feel embarrassed",
           emo_recog = "understand how somebody else is feeling",
           joy = "feel joy",
           morality = "know what's nice and what's mean",
           personality = "have a personality, like when someone is shy and somebody else is silly",
           pleasure = "feel pleasure, like when something feels really good",
           proud = "feel proud"))) %>%
    mutate(short = factor(
      recode(item,
             happy = "happy",
             depressed = "sad",
           fear = "scared",
           angry = "angry",
           calm = "calm",
           sounds = "hear",
           seeing = "see",
           temperature = "temperatures",
           odors = "smell",
           depth = "depth",
           computations = "math",
           thoughts = "thoughts",
           reasoning = "figure out",
           remembering = "remember",
           beliefs = "beliefs",
           hungry = "hungry",
           tired = "tired",
           pain = "pain",
           nauseated = "sick",
           safe = "safe",
           love = "love",
           recognizing = "recognize",
           communicating = "communicate",
           guilt = "guilty",
           disrespected = "hurt feelings",
           free_will = "decide",
           choices = "choices",
           self_restraint = "self-control",
           intentions = "plans",
           goal = "goals",
           conscious = "aware",
           self_aware = "self-aware",
           desires = "desires",
           embarrassed = "embarrassed",
           emo_recog = "empathy",
           joy = "joy",
           morality = "morality",
           personality = "personality",
           pleasure = "pleasure",
           proud = "proud")))

# make dataframe for plotting
scatter_plotting <- loadings(efa_d1_all_rotatedN)[] %>%
  data.frame() %>%
  rownames_to_column(var = "item") %>%
  rename(BODY = MR1,
         HEART = MR2,
         MIND = MR3) %>%
  full_join(wording_s1) %>%
  mutate(dominant = factor(
    ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(BODY), "BODY",
           ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(HEART), "HEART",
                  ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(MIND), "MIND",
                         NA)))),
    size = ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(BODY), abs(BODY),
                  ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(HEART), abs(HEART),
                         ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(MIND), abs(MIND),
                                NA))),
    color = ifelse(dominant == "BODY", "#E41A1C",
                   ifelse(dominant == "HEART", "#377EB8",
                          ifelse(dominant == "MIND", "#4DAF4A",
                                 NA))))

# plot!
figS1 <- plot_ly(scatter_plotting, x = HEART, y = BODY, z = MIND,
             type = "scatter3d",
             color = dominant, colors = c("#377EB8", "#4DAF4A", "#E41A1C"),
             marker = list(size = 4),
             text = short,
             textfont = list(size = 15),
             mode = "text+markers",
             showlegend = TRUE)

figS1
```

### Study 2 (7-9yo)

```{r figure 3d scatter s2}
# set up labels for plot (shortened version of mental capacity items)
wording_s2 <- loadings(efa_d2_all_rotatedN)[] %>%
  data.frame() %>%
  rownames_to_column(var = "item") %>%
  select(item) %>%
  mutate(wording = factor(
    recode(item,
           happy = "feel happy",
           depressed = "feel sad",
           fear = "feel scared",
           angry = "get angry",
           calm = "feel calm",
           sounds = "hear sounds",
           seeing = "see things",
           temperature = "sense temperatures",
           odors = "smell things",
           depth = "sense whether something is close by or far away",
           computations = "do math",
           thoughts = "have thoughts",
           reasoning = "figure out how to do things",
           remembering = "remember things",
           beliefs = "have beliefs, like when you think something is true",
           hungry = "get hungry",
           tired = "feel tired",
           pain = "feel pain",
           nauseated = "feel sick, like when you feel like you might throw up",
           safe = "feel safe",
           love = "feel love",
           recognizing = "recognize somebody else",
           communicating = "communicate with somebody else",
           guilt = "feel guilty",
           disrespected = "get hurt feelings",
           free_will = "decide what to do",
           choices = "make choices",
           self_restraint = "have self-control, like when you stop yourself from doing something you shouldn't do",
           intentions = "make plans",
           goal = "have goals, like when you're working hard to do something or make something happen",
           conscious = "be aware of things",
           self_aware = "be aware of itself",
           desires = "have desires, like when you really want something",
           embarrassed = "feel embarrassed",
           emo_recog = "understand how somebody else is feeling",
           joy = "feel joy",
           morality = "know what's nice and what's mean",
           personality = "have a personality, like when someone is shy and somebody else is silly",
           pleasure = "feel pleasure, like when something feels really good",
           proud = "feel proud"))) %>%
    mutate(short = factor(
      recode(item,
             happy = "happy",
             depressed = "sad",
           fear = "scared",
           angry = "angry",
           calm = "calm",
           sounds = "hear",
           seeing = "see",
           temperature = "temperatures",
           odors = "smell",
           depth = "depth",
           computations = "math",
           thoughts = "thoughts",
           reasoning = "figure out",
           remembering = "remember",
           beliefs = "beliefs",
           hungry = "hungry",
           tired = "tired",
           pain = "pain",
           nauseated = "sick",
           safe = "safe",
           love = "love",
           recognizing = "recognize",
           communicating = "communicate",
           guilt = "guilty",
           disrespected = "hurt feelings",
           free_will = "decide",
           choices = "choices",
           self_restraint = "self-control",
           intentions = "plans",
           goal = "goals",
           conscious = "aware",
           self_aware = "self-aware",
           desires = "desires",
           embarrassed = "embarrassed",
           emo_recog = "empathy",
           joy = "joy",
           morality = "morality",
           personality = "personality",
           pleasure = "pleasure",
           proud = "proud")))

# make dataframe for plotting
scatter_plotting <- loadings(efa_d2_all_rotatedN)[] %>%
  data.frame() %>%
  rownames_to_column(var = "item") %>%
  rename(BODY = MR1,
         HEART = MR2,
         MIND = MR3) %>%
  full_join(wording_s2) %>%
  mutate(dominant = factor(
    ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(BODY), "BODY",
           ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(HEART), "HEART",
                  ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(MIND), "MIND",
                         NA)))),
    size = ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(BODY), abs(BODY),
                  ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(HEART), abs(HEART),
                         ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(MIND), abs(MIND),
                                NA))),
    color = ifelse(dominant == "BODY", "#E41A1C",
                   ifelse(dominant == "HEART", "#4DAF4A",
                          ifelse(dominant == "MIND", "#E41A1C",
                                 NA))))

# plot!
figS2 <- plot_ly(scatter_plotting, x = HEART, y = BODY, z = MIND,
             type = "scatter3d",
             color = dominant, colors = c("#377EB8", "#4DAF4A", "#E41A1C"),
             marker = list(size = 4),
             text = short,
             textfont = list(size = 15),
             mode = "text+markers",
             showlegend = TRUE)

figS2
```

### Study 3 (7-9yo)

```{r figure 3d scatter s3}
# set up labels for plot (shortened version of mental capacity items)
wording_s3 <- loadings(efa_d3_all_rotatedN)[] %>%
  data.frame() %>%
  rownames_to_column(var = "item") %>%
  select(item) %>%
  mutate(wording = factor(
    recode(item,
           happy = "feel happy",
           depressed = "feel sad",
           fear = "feel scared",
           angry = "get angry",
           calm = "feel calm",
           sounds = "hear sounds",
           seeing = "see things",
           temperature = "sense temperatures",
           odors = "smell things",
           depth = "sense whether something is close by or far away",
           computations = "do math",
           thoughts = "have thoughts",
           reasoning = "figure out how to do things",
           remembering = "remember things",
           beliefs = "have beliefs, like when you think something is true",
           hungry = "get hungry",
           tired = "feel tired",
           pain = "feel pain",
           nauseated = "feel sick, like when you feel like you might throw up",
           safe = "feel safe",
           love = "feel love",
           recognizing = "recognize somebody else",
           communicating = "communicate with somebody else",
           guilt = "feel guilty",
           disrespected = "get hurt feelings",
           free_will = "decide what to do",
           choices = "make choices",
           self_restraint = "have self-control, like when you stop yourself from doing something you shouldn't do",
           intentions = "make plans",
           goal = "have goals, like when you're working hard to do something or make something happen",
           conscious = "be aware of things",
           self_aware = "be aware of itself",
           desires = "have desires, like when you really want something",
           embarrassed = "feel embarrassed",
           emo_recog = "understand how somebody else is feeling",
           joy = "feel joy",
           morality = "know what's nice and what's mean",
           personality = "have a personality, like when someone is shy and somebody else is silly",
           pleasure = "feel pleasure, like when something feels really good",
           proud = "feel proud"))) %>%
    mutate(short = factor(
      recode(item,
             happy = "happy",
             depressed = "sad",
           fear = "scared",
           angry = "angry",
           calm = "calm",
           sounds = "hear",
           seeing = "see",
           temperature = "temperatures",
           odors = "smell",
           depth = "depth",
           computations = "math",
           thoughts = "thoughts",
           reasoning = "figure out",
           remembering = "remember",
           beliefs = "beliefs",
           hungry = "hungry",
           tired = "tired",
           pain = "pain",
           nauseated = "sick",
           safe = "safe",
           love = "love",
           recognizing = "recognize",
           communicating = "communicate",
           guilt = "guilty",
           disrespected = "hurt feelings",
           free_will = "decide",
           choices = "choices",
           self_restraint = "self-control",
           intentions = "plans",
           goal = "goals",
           conscious = "aware",
           self_aware = "self-aware",
           desires = "desires",
           embarrassed = "embarrassed",
           emo_recog = "empathy",
           joy = "joy",
           morality = "morality",
           personality = "personality",
           pleasure = "pleasure",
           proud = "proud")))

# make dataframe for plotting
scatter_plotting <- loadings(efa_d3_all_rotatedN)[] %>%
  data.frame() %>%
  rownames_to_column(var = "item") %>%
  rename(BODY = MR1,
         HEART = MR2,
         MIND = MR3) %>%
  full_join(wording_s3) %>%
  mutate(dominant = factor(
    ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(BODY), "BODY",
           ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(HEART), "HEART",
                  ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(MIND), "MIND",
                         NA)))),
    size = ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(BODY), abs(BODY),
                  ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(HEART), abs(HEART),
                         ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(MIND), abs(MIND),
                                NA))),
    color = ifelse(dominant == "BODY", "#E41A1C",
                   ifelse(dominant == "HEART", "#4DAF4A",
                          ifelse(dominant == "MIND", "#E41A1C",
                                 NA))))

# plot!
figs3 <- plot_ly(scatter_plotting, x = HEART, y = BODY, z = MIND,
             type = "scatter3d",
             color = dominant, colors = c("#377EB8", "#4DAF4A", "#E41A1C"),
             marker = list(size = 4),
             text = short,
             textfont = list(size = 15),
             mode = "text+markers",
             showlegend = TRUE)

figs3
```

### Study 4 (4-6yo)

```{r figure 3d scatter s4}
# set up labels for plot (shortened version of mental capacity items)
wording_s4 <- loadings(efa_d4_all_rotatedN)[] %>%
  data.frame() %>%
  rownames_to_column(var = "item") %>%
  select(item) %>%
  mutate(wording = factor(
    recode(item,
           happy = "feel happy",
           depressed = "feel sad",
           fear = "feel scared",
           angry = "get angry",
           calm = "feel calm",
           sounds = "hear sounds",
           seeing = "see things",
           temperature = "sense temperatures",
           odors = "smell things",
           depth = "sense whether something is close by or far away",
           computations = "do math",
           thoughts = "have thoughts",
           reasoning = "figure out how to do things",
           remembering = "remember things",
           beliefs = "have beliefs, like when you think something is true",
           hungry = "get hungry",
           tired = "feel tired",
           pain = "feel pain",
           nauseated = "feel sick, like when you feel like you might throw up",
           safe = "feel safe",
           love = "feel love",
           recognizing = "recognize somebody else",
           communicating = "communicate with somebody else",
           guilt = "feel guilty",
           disrespected = "get hurt feelings",
           free_will = "decide what to do",
           choices = "make choices",
           self_restraint = "have self-control, like when you stop yourself from doing something you shouldn't do",
           intentions = "make plans",
           goal = "have goals, like when you're working hard to do something or make something happen",
           conscious = "be aware of things",
           self_aware = "be aware of itself",
           desires = "have desires, like when you really want something",
           embarrassed = "feel embarrassed",
           emo_recog = "understand how somebody else is feeling",
           joy = "feel joy",
           morality = "know what's nice and what's mean",
           personality = "have a personality, like when someone is shy and somebody else is silly",
           pleasure = "feel pleasure, like when something feels really good",
           proud = "feel proud"))) %>%
    mutate(short = factor(
      recode(item,
             happy = "happy",
             depressed = "sad",
           fear = "scared",
           angry = "angry",
           calm = "calm",
           sounds = "hear",
           seeing = "see",
           temperature = "temperatures",
           odors = "smell",
           depth = "depth",
           computations = "math",
           thoughts = "thoughts",
           reasoning = "figure out",
           remembering = "remember",
           beliefs = "beliefs",
           hungry = "hungry",
           tired = "tired",
           pain = "pain",
           nauseated = "sick",
           safe = "safe",
           love = "love",
           recognizing = "recognize",
           communicating = "communicate",
           guilt = "guilty",
           disrespected = "hurt feelings",
           free_will = "decide",
           choices = "choices",
           self_restraint = "self-control",
           intentions = "plans",
           goal = "goals",
           conscious = "aware",
           self_aware = "self-aware",
           desires = "desires",
           embarrassed = "embarrassed",
           emo_recog = "empathy",
           joy = "joy",
           morality = "morality",
           personality = "personality",
           pleasure = "pleasure",
           proud = "proud")))

# make dataframe for plotting
scatter_plotting <- loadings(efa_d4_all_rotatedN)[] %>%
  data.frame() %>%
  rownames_to_column(var = "item") %>%
  rename(BODY = MR1,
         HEART = MR2,
         MIND = MR3) %>%
  full_join(wording_s4) %>%
  mutate(dominant = factor(
    ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(BODY), "BODY",
           ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(HEART), "HEART",
                  ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(MIND), "MIND",
                         NA)))),
    size = ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(BODY), abs(BODY),
                  ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(HEART), abs(HEART),
                         ifelse(pmax(abs(BODY), abs(HEART), abs(MIND)) == abs(MIND), abs(MIND),
                                NA))),
    color = ifelse(dominant == "BODY", "#E41A1C",
                   ifelse(dominant == "HEART", "#4DAF4A",
                          ifelse(dominant == "MIND", "#E41A1C",
                                 NA))))

# plot!
figs4 <- plot_ly(scatter_plotting, x = HEART, y = BODY, z = MIND,
             type = "scatter3d",
             color = dominant, colors = c("#377EB8", "#4DAF4A", "#E41A1C"),
             marker = list(size = 4),
             text = short,
             textfont = list(size = 15),
             mode = "text+markers",
             showlegend = TRUE)

figs4
```

## Heatmaps

*NOTE: set to 3 factors manually, for now.*

### Study 1 (adults)

```{r figure heatmap s1, fig.width = 14, fig.height = 14}
factors_s1 <- fa.sort(fa(d1_all, nfactors = 3, cor = chosenCorType, rotate = chosenRotType)$loadings[]) %>%
  data.frame() %>%
  rownames_to_column(var = "item") %>%
  full_join(wording_s1) %>%
  select(wording, MR1, MR2, MR3) %>%
  rename(capacity = wording, Factor1 = MR1, Factor2 = MR2, Factor3 = MR3) %>%
  rownames_to_column(var = "order") %>%
  mutate(order = as.numeric(order))

factors_s1_long <- factors_s1 %>%
  gather(factor, loading, -capacity, -order) %>%
  mutate(factor = factor(gsub("Factor", "F", factor))) %>%
  # mutate(factor = factor(gsub("Factor", "F", factor),
  #                        levels = c("F1", "F3", "F2"))) %>%
  mutate(factor = factor(gsub("Factor", "F", factor),
                         levels = c("F2", "F1", "F3"))) %>%
  arrange(order, factor)

factors_s1_blank1 <- factors_s1_long %>%
  mutate(loading = rep(100, length(factors_s1_long$loading)))
# factors_s1_blank2 <- factors_s1_long %>%
#   mutate(loading = ifelse(factor == "F1", loading, rep(100, length(factors_s1_long$loading)*2/3)))
factors_s1_blank2 <- factors_s1_long %>%
  mutate(loading = ifelse(factor == "F2", loading, rep(100, length(factors_s1_long$loading)*2/3)))
factors_s1_blank3 <- factors_s1_long %>%
  mutate(loading = ifelse(factor != "F3", loading, rep(100, length(factors_s1_long$loading)*1/3)))

# ggplot(factors_s1_blank1, aes(x = factor,
#                             y = reorder(capacity, desc(order)), fill = loading)) +
#   geom_tile(color = "black") +
#   # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
#   scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
#                        guide = guide_colorbar(title = element_blank(),
#                                               barheight = 20)) +
#   scale_x_discrete(position = "top") +
#   theme_minimal() +
#   theme(text = element_text(size = 24),
#         axis.text.x = element_text(size = 28),
#         axis.title = element_blank(),
#         panel.grid = element_blank()) # 1000 by 1000
# 
# ggplot(factors_s1_blank2, aes(x = factor,
#                               y = reorder(capacity, desc(order)), fill = loading)) +
#   geom_tile(color = "black") +
#   # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
#   scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
#                        guide = guide_colorbar(title = element_blank(),
#                                               barheight = 20)) +
#   scale_x_discrete(position = "top") +
#   theme_minimal() +
#   theme(text = element_text(size = 24),
#         axis.text.x = element_text(size = 28),
#         axis.title = element_blank(),
#         panel.grid = element_blank()) # 1000 by 1000
# 
# ggplot(factors_s1_blank3, aes(x = factor,
#                               y = reorder(capacity, desc(order)), fill = loading)) +
#   geom_tile(color = "black") +
#   # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
#   scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
#                        guide = guide_colorbar(title = element_blank(),
#                                               barheight = 20)) +
#   scale_x_discrete(position = "top") +
#   theme_minimal() +
#   theme(text = element_text(size = 24),
#         axis.text.x = element_text(size = 28),
#         axis.title = element_blank(),
#         panel.grid = element_blank()) # 1000 by 1000

ggplot(factors_s1_long, aes(x = factor,
                            y = reorder(capacity, desc(order)), fill = loading)) +
  geom_tile(color = "black") +
  # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
  scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
                       guide = guide_colorbar(title = element_blank(),
                                              barheight = 20)) +
  scale_x_discrete(position = "top") +
  # geom_rect(aes(xmin = 0.51, xmax = 1.49, ymin = 14.55, ymax = 20.45),
  #           alpha = 0, color = "black", size = .5) +
  # geom_rect(aes(xmin = 1.51, xmax = 2.49, ymin = 6.55, ymax = 14.45),
  #           alpha = 0, color = "black", size = .5) +
  # geom_rect(aes(xmin = 2.51, xmax = 3.49, ymin = 0.55, ymax = 6.45),
  #           alpha = 0, color = "black", size = .5) +
  # theme_bw() +
  theme_minimal() +
  theme(text = element_text(size = 24),
        axis.text.x = element_text(size = 28),
        axis.title = element_blank(),
        panel.grid = element_blank()) # 1000 by 1000
```

### Study 2 (7-9y)

```{r figure heatmap s2, fig.width = 14, fig.height = 14}
factors_s2 <- fa.sort(fa(d2_all, nfactors = 3, cor = chosenCorType, rotate = chosenRotType)$loadings[]) %>%
  data.frame() %>%
  rownames_to_column(var = "item") %>%
  full_join(wording_s2) %>%
  select(wording, MR1, MR2, MR3) %>%
  rename(capacity = wording, Factor1 = MR1, Factor2 = MR2, Factor3 = MR3) %>%
  rownames_to_column(var = "order") %>%
  mutate(order = as.numeric(order))

factors_s2_long <- factors_s2 %>%
  gather(factor, loading, -capacity, -order) %>%
  mutate(factor = factor(gsub("Factor", "F", factor))) %>%
  # mutate(factor = factor(gsub("Factor", "F", factor),
  #                        levels = c("F1", "F3", "F2"))) %>%
  # mutate(factor = factor(gsub("Factor", "F", factor),
  #                        levels = c("F2", "F1", "F3"))) %>%
  arrange(order, factor)

factors_s2_blank1 <- factors_s2_long %>%
  mutate(loading = rep(100, length(factors_s2_long$loading)))
factors_s2_blank2 <- factors_s2_long %>%
  mutate(loading = ifelse(factor == "F1", loading, rep(100, length(factors_s2_long$loading)*2/3)))
# factors_s2_blank2 <- factors_s2_long %>%
#   mutate(loading = ifelse(factor == "F2", loading, rep(100, length(factors_s2_long$loading)*2/3)))
factors_s2_blank3 <- factors_s2_long %>%
  mutate(loading = ifelse(factor != "F3", loading, rep(100, length(factors_s2_long$loading)*1/3)))

# ggplot(factors_s2_blank1, aes(x = factor,
#                             y = reorder(capacity, desc(order)), fill = loading)) +
#   geom_tile(color = "black") +
#   # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
#   scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
#                        guide = guide_colorbar(title = element_blank(),
#                                               barheight = 20)) +
#   scale_x_discrete(position = "top") +
#   theme_minimal() +
#   theme(text = element_text(size = 24),
#         axis.text.x = element_text(size = 28),
#         axis.title = element_blank(),
#         panel.grid = element_blank()) # 1000 by 1000
# 
# ggplot(factors_s2_blank2, aes(x = factor,
#                               y = reorder(capacity, desc(order)), fill = loading)) +
#   geom_tile(color = "black") +
#   # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
#   scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
#                        guide = guide_colorbar(title = element_blank(),
#                                               barheight = 20)) +
#   scale_x_discrete(position = "top") +
#   theme_minimal() +
#   theme(text = element_text(size = 24),
#         axis.text.x = element_text(size = 28),
#         axis.title = element_blank(),
#         panel.grid = element_blank()) # 1000 by 1000
# 
# ggplot(factors_s2_blank3, aes(x = factor,
#                               y = reorder(capacity, desc(order)), fill = loading)) +
#   geom_tile(color = "black") +
#   # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
#   scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
#                        guide = guide_colorbar(title = element_blank(),
#                                               barheight = 20)) +
#   scale_x_discrete(position = "top") +
#   theme_minimal() +
#   theme(text = element_text(size = 24),
#         axis.text.x = element_text(size = 28),
#         axis.title = element_blank(),
#         panel.grid = element_blank()) # 1000 by 1000

ggplot(factors_s2_long, aes(x = factor,
                            y = reorder(capacity, desc(order)), fill = loading)) +
  geom_tile(color = "black") +
  # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
  scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
                       guide = guide_colorbar(title = element_blank(),
                                              barheight = 20)) +
  scale_x_discrete(position = "top") +
  # geom_rect(aes(xmin = 0.51, xmax = 1.49, ymin = 14.55, ymax = 20.45),
  #           alpha = 0, color = "black", size = .5) +
  # geom_rect(aes(xmin = 1.51, xmax = 2.49, ymin = 6.55, ymax = 14.45),
  #           alpha = 0, color = "black", size = .5) +
  # geom_rect(aes(xmin = 2.51, xmax = 3.49, ymin = 0.55, ymax = 6.45),
  #           alpha = 0, color = "black", size = .5) +
  # theme_bw() +
  theme_minimal() +
  theme(text = element_text(size = 24),
        axis.text.x = element_text(size = 28),
        axis.title = element_blank(),
        panel.grid = element_blank()) # 1000 by 1000
```

### Study 3 (7-9y)

```{r figure heatmap s3, fig.width = 10, fig.height = 8}
factors_s3 <- fa.sort(fa(d3_all, nfactors = 3, cor = chosenCorType, rotate = chosenRotType)$loadings[]) %>%
  data.frame() %>%
  rownames_to_column(var = "item") %>%
  left_join(wording_s3) %>%
  select(wording, MR1, MR2, MR3) %>%
  rename(capacity = wording, Factor1 = MR1, Factor2 = MR2, Factor3 = MR3) %>%
  rownames_to_column(var = "order") %>%
  mutate(order = as.numeric(order))

factors_s3_long <- factors_s3 %>%
  gather(factor, loading, -capacity, -order) %>%
  mutate(factor = factor(gsub("Factor", "F", factor))) %>%
  # mutate(factor = factor(gsub("Factor", "F", factor),
  #                        levels = c("F1", "F3", "F2"))) %>%
  mutate(factor = factor(gsub("Factor", "F", factor),
                         levels = c("F2", "F1", "F3"))) %>%
  arrange(order, factor)

factors_s3_blank1 <- factors_s3_long %>%
  mutate(loading = rep(100, length(factors_s3_long$loading)))
# factors_s3_blank2 <- factors_s3_long %>%
#   mutate(loading = ifelse(factor == "F1", loading, rep(100, length(factors_s3_long$loading)*2/3)))
factors_s3_blank2 <- factors_s3_long %>%
  mutate(loading = ifelse(factor == "F2", loading, rep(100, length(factors_s3_long$loading)*2/3)))
factors_s3_blank3 <- factors_s3_long %>%
  mutate(loading = ifelse(factor != "F3", loading, rep(100, length(factors_s3_long$loading)*1/3)))

# ggplot(factors_s3_blank1, aes(x = factor,
#                             y = reorder(capacity, desc(order)), fill = loading)) +
#   geom_tile(color = "black") +
#   # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
#   scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
#                        guide = guide_colorbar(title = element_blank(),
#                                               barheight = 20)) +
#   scale_x_discrete(position = "top") +
#   theme_minimal() +
#   theme(text = element_text(size = 24),
#         axis.text.x = element_text(size = 28),
#         axis.title = element_blank(),
#         panel.grid = element_blank()) # 1000 by 1000
# 
# ggplot(factors_s3_blank2, aes(x = factor,
#                               y = reorder(capacity, desc(order)), fill = loading)) +
#   geom_tile(color = "black") +
#   # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
#   scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
#                        guide = guide_colorbar(title = element_blank(),
#                                               barheight = 20)) +
#   scale_x_discrete(position = "top") +
#   theme_minimal() +
#   theme(text = element_text(size = 24),
#         axis.text.x = element_text(size = 28),
#         axis.title = element_blank(),
#         panel.grid = element_blank()) # 1000 by 1000
# 
# ggplot(factors_s3_blank3, aes(x = factor,
#                               y = reorder(capacity, desc(order)), fill = loading)) +
#   geom_tile(color = "black") +
#   # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
#   scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
#                        guide = guide_colorbar(title = element_blank(),
#                                               barheight = 20)) +
#   scale_x_discrete(position = "top") +
#   theme_minimal() +
#   theme(text = element_text(size = 24),
#         axis.text.x = element_text(size = 28),
#         axis.title = element_blank(),
#         panel.grid = element_blank()) # 1000 by 1000

ggplot(factors_s3_long, aes(x = factor,
                            y = reorder(capacity, desc(order)), fill = loading)) +
  geom_tile(color = "black") +
  # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
  scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
                       guide = guide_colorbar(title = element_blank(),
                                              barheight = 20)) +
  scale_x_discrete(position = "top") +
  # geom_rect(aes(xmin = 0.51, xmax = 1.49, ymin = 14.55, ymax = 20.45),
  #           alpha = 0, color = "black", size = .5) +
  # geom_rect(aes(xmin = 1.51, xmax = 2.49, ymin = 6.55, ymax = 14.45),
  #           alpha = 0, color = "black", size = .5) +
  # geom_rect(aes(xmin = 2.51, xmax = 3.49, ymin = 0.55, ymax = 6.45),
  #           alpha = 0, color = "black", size = .5) +
  # theme_bw() +
  theme_minimal() +
  theme(text = element_text(size = 24),
        axis.text.x = element_text(size = 28),
        axis.title = element_blank(),
        panel.grid = element_blank()) # 1000 by 1000
```

### Study 4 (4-6y)

```{r figure heatmap s4, fig.width = 10, fig.height = 8}
factors_s4 <- fa.sort(fa(d4_all, nfactors = 3, cor = chosenCorType, rotate = chosenRotType)$loadings[]) %>%
  data.frame() %>%
  rownames_to_column(var = "item") %>%
  left_join(wording_s4) %>%
  select(wording, MR1, MR2, MR3) %>%
  rename(capacity = wording, Factor1 = MR1, Factor2 = MR2, Factor3 = MR3) %>%
  rownames_to_column(var = "order") %>%
  mutate(order = as.numeric(order))

factors_s4_long <- factors_s4 %>%
  gather(factor, loading, -capacity, -order) %>%
  mutate(factor = factor(gsub("Factor", "F", factor))) %>%
  # mutate(factor = factor(gsub("Factor", "F", factor),
  #                        levels = c("F1", "F3", "F2"))) %>%
  mutate(factor = factor(gsub("Factor", "F", factor),
                         levels = c("F2", "F1", "F3"))) %>%
  arrange(order, factor)

factors_s4_blank1 <- factors_s4_long %>%
  mutate(loading = rep(100, length(factors_s4_long$loading)))
# factors_s4_blank2 <- factors_s4_long %>%
#   mutate(loading = ifelse(factor == "F1", loading, rep(100, length(factors_s4_long$loading)*2/3)))
factors_s4_blank2 <- factors_s4_long %>%
  mutate(loading = ifelse(factor == "F2", loading, rep(100, length(factors_s4_long$loading)*2/3)))
factors_s4_blank3 <- factors_s4_long %>%
  mutate(loading = ifelse(factor != "F3", loading, rep(100, length(factors_s4_long$loading)*1/3)))

# ggplot(factors_s4_blank1, aes(x = factor,
#                             y = reorder(capacity, desc(order)), fill = loading)) +
#   geom_tile(color = "black") +
#   # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
#   scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
#                        guide = guide_colorbar(title = element_blank(),
#                                               barheight = 20)) +
#   scale_x_discrete(position = "top") +
#   theme_minimal() +
#   theme(text = element_text(size = 24),
#         axis.text.x = element_text(size = 28),
#         axis.title = element_blank(),
#         panel.grid = element_blank()) # 1000 by 1000
# 
# ggplot(factors_s4_blank2, aes(x = factor,
#                               y = reorder(capacity, desc(order)), fill = loading)) +
#   geom_tile(color = "black") +
#   # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
#   scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
#                        guide = guide_colorbar(title = element_blank(),
#                                               barheight = 20)) +
#   scale_x_discrete(position = "top") +
#   theme_minimal() +
#   theme(text = element_text(size = 24),
#         axis.text.x = element_text(size = 28),
#         axis.title = element_blank(),
#         panel.grid = element_blank()) # 1000 by 1000
# 
# ggplot(factors_s4_blank3, aes(x = factor,
#                               y = reorder(capacity, desc(order)), fill = loading)) +
#   geom_tile(color = "black") +
#   # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
#   scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
#                        guide = guide_colorbar(title = element_blank(),
#                                               barheight = 20)) +
#   scale_x_discrete(position = "top") +
#   theme_minimal() +
#   theme(text = element_text(size = 24),
#         axis.text.x = element_text(size = 28),
#         axis.title = element_blank(),
#         panel.grid = element_blank()) # 1000 by 1000

ggplot(factors_s4_long, aes(x = factor,
                            y = reorder(capacity, desc(order)), fill = loading)) +
  geom_tile(color = "black") +
  # geom_text(aes(label = format(round(loading, 2), nsmall = 2))) +
  scale_fill_distiller(palette = "RdYlBu", limits = c(-1, 1), breaks = c(-1, 0, 1),
                       guide = guide_colorbar(title = element_blank(),
                                              barheight = 20)) +
  scale_x_discrete(position = "top") +
  # geom_rect(aes(xmin = 0.51, xmax = 1.49, ymin = 14.55, ymax = 20.45),
  #           alpha = 0, color = "black", size = .5) +
  # geom_rect(aes(xmin = 1.51, xmax = 2.49, ymin = 6.55, ymax = 14.45),
  #           alpha = 0, color = "black", size = .5) +
  # geom_rect(aes(xmin = 2.51, xmax = 3.49, ymin = 0.55, ymax = 6.45),
  #           alpha = 0, color = "black", size = .5) +
  # theme_bw() +
  theme_minimal() +
  theme(text = element_text(size = 24),
        axis.text.x = element_text(size = 28),
        axis.title = element_blank(),
        panel.grid = element_blank()) # 1000 by 1000
```

## Mean ratings

### Studies 1-2

Mean ratings of 40 mental capacities for the 2 entities included in Studies 1-2. Participants responded on a 3-point scale (0 = "no", 0.5 = "kinda", 1 = "yes"). Error bars are nonparametric bootstrapped 95% confidence intervals. Mental capacities are grouped according to their dominant factor loading in Study 1 (adults).

```{r figure mean ratings s1-s2, fig.width = 6, fig.height = 6}
# make dataframe
s12_plotting <- char_plotting %>%
  filter(study %in% c("study 1", "study 2")) %>%
  distinct()

# plot! (ordered by study 3 factor loadings)
s12 <- ggplot(s12_plotting,
               aes(y = mean_na, x = reorder(wording, desc(s1_order)), colour = factor(s1_color),
                   shape = study)) +
  geom_point(stat = "identity", position = position_dodge(width = 0.6), size = 2) +
  geom_errorbar(aes(ymin = ci_lower_na, ymax = ci_upper_na), width = 0.4,
                position = position_dodge(width = 0.6)) +
  facet_wrap(~ character) +
  theme_bw() +
  scale_y_continuous(name = "\nMean rating",
                     limits = c(0, 1),
                     breaks = c(0, 0.5, 1),
                     labels = c("0\n(no)", "0.5\n(kinda)", "1\n(yes)")) +
  scale_shape_discrete(name = "Study:",
                       labels = c("Study 1: adults", "Study 2: 7-9y")) +
  # scale_colour_brewer(name = "Factor:",
  #                     type = "qual", palette = 6,
  #                     guide = FALSE) +
  scale_colour_manual(name = "Factor:",
                      values = c("#377EB8", "#4DAF4A", "#E41A1C"),
                      labels = c("HEART", "MIND", "BODY")) +
  coord_flip() +
  theme(text = element_text(size = 9),
      axis.title.y = element_blank(),
      axis.text.y = element_text(face = "italic",
                                 colour = palette_s1),
      panel.grid.minor = element_blank(),
      legend.position = "right")

s12
```

### Studies 3-4

Mean ratings of 20 mental capacities for the 9 entities included in Studies 3-4. Participants responded on a 3-point scale (0 = "no", 0.5 = "kinda", 1 = "yes"). Error bars are nonparametric bootstrapped 95% confidence intervals. Mental capacities are grouped according to their dominant factor loading in Study 3 (7-9y).

```{r figure mean ratings s3-s4, fig.width = 10, fig.height = 6}
# make dataframe
s34_plotting <- char_plotting %>%
  filter(study %in% c("study 3", "study 4"),
         !is.na(s3_order), !is.na(character), !is.na(capacity)) %>%
  distinct() %>%
  mutate(character = factor(character,
                            levels = c("computer", "doll", "teddy_bear", "robot", 
                                       "beetle", "bird", "mouse", "goat", "elephant")))

# plot! (ordered by study 3 factor loadings)
s34 <- ggplot(s34_plotting,
               aes(y = mean_na, x = reorder(wording, desc(s3_order)), 
                   # colour = study,
                   colour = s3_color,
                   shape = study)) +
  geom_point(stat = "identity", position = position_dodge(width = 0.6), size = 2) +
  geom_errorbar(aes(ymin = ci_lower_na, ymax = ci_upper_na), width = 0.4,
                position = position_dodge(width = 0.6)) +
  facet_wrap(~ character, ncol = 9) +
  theme_bw() +
  scale_y_continuous(name = "\nMean rating",
                     limits = c(0, 1),
                     breaks = c(0, 0.5, 1),
                     labels = c("0\n(no)", "0.5\n(kinda)", "1\n(yes)")) +
  scale_shape_discrete(name = "Study:",
                       labels = c("Study 3: 7-9y", "Study 4: 4-6y")) +
  # scale_colour_discrete(name = "Study:",
  #                      labels = c("Study 3: 7-9y", "Study 4: 4-6y")) +
  # scale_colour_brewer(name = "Factor:",
  #                     type = "qual", palette = 6,
  #                     guide = FALSE) +
  scale_colour_manual(name = "Factor:",
                      values = c("#377EB8", "#4DAF4A", "#E41A1C"),
                      labels = c("HEART", "MIND", "BODY")) +
  coord_flip() +
  theme(text = element_text(size = 9),
      axis.title.y = element_blank(),
      axis.text.y = element_text(face = "italic"),
                                 # colour = palette_s1),
      panel.grid.minor = element_blank(),
      legend.position = "bottom")

s34
```

# Mean factor scores

## Studies 1-2

```{r s12 all no rotation, include = F}
# make combined dataset
d12_all <- d1_all %>% rownames_to_column("subid") %>%
  full_join(d2_all %>% rownames_to_column("subid")) %>%
  column_to_rownames("subid")

# examine scree plot
fa.parallel(d12_all)

# run EFA without rotation with N factors
efa_d12_all_unrotated <- fa(d12_all, 13, rotate = "none",
                           cor = chosenCorType, fm = "minres")
print(efa_d12_all_unrotated)

# examine eigenvalues and variance explained
efa_d12_all_unrotated_eigenvalues <- print(efa_d12_all_unrotated)$Vaccounted %>%
  t() %>%
  data.frame()

# count factors with eigenvalues > 1 and variance explained > 5%
efa_d12_all_unrotated_nfactors <- efa_d12_all_unrotated_eigenvalues %>%
  filter(SS.loadings > 1, Proportion.Explained > 0.05) %>%
  count() %>%
  as.numeric()
efa_d12_all_unrotated_nfactors
```

```{r s12 all rotation, include = F}
efa_d12_all_rotated_max <- fa(d12_all, 13, rotate = chosenRotType,
                           cor = chosenCorType, fm = "minres")

efa_d12_all_rotated <- fa(d12_all, efa_d12_all_unrotated_nfactors, rotate = chosenRotType,
                           cor = chosenCorType, fm = "minres")

# check that each of these factors is the dominant factor for at least one mental capacity item
efa_d12_all_rotated_loadings <- fa.sort(loadings(efa_d12_all_rotated)[]) %>%
  data.frame() %>%
  rownames_to_column("capacity") %>%
  gather(factor, loading, -capacity) %>%
  mutate(loading_abs = abs(loading)) %>%
  group_by(capacity) %>%
  top_n(1, loading_abs) %>%
  ungroup()
efa_d12_all_rotated_loadings

# drop any factors where n < 1
efa_d12_all_rotated_loadings %>% 
  count(factor) %>% 
  filter(n > 0)

# set number of factors to extract
nfactors_d12_all <- efa_d12_all_rotated_loadings %>% 
  count(factor) %>% 
  filter(n > 0) %>%
  nrow()
nfactors_d12_all
```

```{r s12 all varimax rotation, include = F}
# run EFA with rotation with N factors
efa_d12_all_rotatedN <- fa(d12_all, nfactors_d12_all, 
                          rotate = chosenRotType, cor = chosenCorType, fm = "minres",
                          scores = "tenBerge", missing = TRUE) # impute missing values
print(efa_d12_all_rotatedN)

# get loadings for each factor
efa_d12_all_rotatedN_loadings <- loadings(efa_d12_all_rotatedN)[] %>%
  data.frame() %>% 
  rownames_to_column(var = "capacity")
```

```{r s12 loadings table, include = F}
data.frame(loadings(fa.sort(efa_d12_all_rotatedN))[]) %>%
  rownames_to_column("capacity") %>%
  mutate_at(vars(starts_with("M")), funs(round2))
```

```{r s12 figure setup, include = F}
scores_s12_plotting <- d1 %>% 
  select(subid, age_group, character) %>% 
  distinct() %>% 
  mutate(subid = paste(character, subid, sep = "_")) %>%
  full_join(d2 %>% 
              select(subid, age_group, character) %>% 
              distinct() %>% 
              mutate(subid = paste(character, subid, sep = "_"))) %>%
  full_join(efa_d12_all_rotatedN$scores %>% 
              data.frame() %>% 
              rownames_to_column("subid")) %>%
  mutate(character = factor(character)) %>%
  rename(score_F1 = MR1, score_F2 = MR2, score_F3 = MR3) %>%
  filter(!is.na(score_F1), !is.na(score_F2), !is.na(score_F3), !is.na(age_group)) %>%
  gather(factor, score, starts_with("score_")) %>%
  mutate(factor = factor(factor)) %>%
  multi_boot(column = "score",
             summary_groups = c("age_group", "character", "factor"),
             statistics_functions = c("mean", "ci_lower", "ci_upper"))
```

```{r s12 regression}
tempC <- d1 %>% mutate(subid = paste(character, subid, sep = "_")) %>%
  full_join(d2 %>% mutate(subid = paste(character, subid, sep = "_"))) %>%
  full_join(data.frame(efa_d12_all_rotatedN$scores) %>%
            rownames_to_column("subid") %>%
              gather(factor, score, -subid)) %>%
  mutate(factor = factor(factor),
         age_group = factor(age_group),
         character = factor(character)) # %>%
  # filter(!is.na(factor), !is.na(age_group), !is.na(character))

contrasts(tempC$factor) = cbind(factor1 = c(1, -1, 0),
                                factor3 = c(0, -1, 1))

contrasts(tempC$age_group) = cbind(children = c(-1, 1))
contrasts(tempC$character) = cbind(robot = c(-1, 1))

library(lme4)
r1 <- lmer(score ~ character * factor * age_group + (1 | subid) , tempC)
summary(r1)

# library(brms)
# r1b <- brm(score ~ character * factor * age_group + (1 | subid) , tempC,
#             family = "gaussian")
# summary(r1b)
```

```{r s12 figure factor scores by age group, fig.width = 12, fig.height = 6}
# plot
ggplot(scores_s12_plotting %>%
         ungroup() %>%
         mutate(factor = factor(factor,
                                labels = c("Social-emotional",
                                           "Bodily",
                                           "Perceptual-cognitive")),
                age_group = factor(age_group,
                                  # levels = c("adults", "children_79"),
                                  # labels = c("adults", "children"))),
                                  levels = c("children_79", "adults"),
                                  labels = c("children", "adults"))),
       aes(x = age_group, y = mean, color = character, shape = character)) +
  facet_wrap("factor", ncol = 3) +
  theme_bw() +
  theme(text = element_text(size = 28),
        legend.position = "bottom") +
  geom_point(size = 5, position = position_dodge(width = 0.4)) +
  geom_errorbar(aes(ymin = ci_lower, ymax = ci_upper),
                width = 0.2, position = position_dodge(width = 0.4)) +
  scale_shape_manual(values = c(19, 15)) +
  labs(title = "Factor scores by age group",
       # subtitle = "Adults (Study 1) vs. children (Study 2)\n",
       x = "Age group",
       y = "Mean factor score") # 1000 by 500
```

## Study 3

```{r s3 figure setup, include = F}
scores_s3_plotting <- d3 %>% 
  select(subid, age_group, character) %>% 
  distinct() %>% 
  mutate(subid = paste(character, subid, sep = "_")) %>%
  full_join(efa_d3_all_rotatedN$scores %>% 
              data.frame() %>% 
              rownames_to_column("subid")) %>%
  mutate(character = factor(character)) %>%
  rename(score_F1 = MR1, score_F2 = MR2, score_F3 = MR3) %>%
  filter(!is.na(score_F1), !is.na(score_F2), !is.na(score_F3), !is.na(age_group)) %>%
  gather(factor, score, starts_with("score_")) %>%
  mutate(factor = factor(factor)) %>%
  multi_boot(column = "score",
             summary_groups = c("age_group", "character", "factor"),
             statistics_functions = c("mean", "ci_lower", "ci_upper"))
```

```{r s3 figure factor scores by character, fig.width = 12, fig.height = 6}
ggplot(scores_s3_plotting %>%
         ungroup() %>%
         mutate(character = factor(character, 
                                   levels = c("computer", "robot", "doll", "teddy_bear",
                                              "beetle", "bird", "mouse", "goat", "elephant"),
                                   labels = c("computer", "robot", "doll", "teddy bear",
                                              "beetle", "bird", "mouse", "goat", "elephant")),
                factor = factor(factor,
                                levels = c("score_F2", "score_F1", "score_F3"),
                                labels = c("Social-emotional", "Bodily", "Perceptual-cognitive"))),
       aes(x = character, y = mean, color = character, shape = character)) +
  facet_wrap(~ factor, ncol = 3) +
  theme_bw() +
  theme(text = element_text(size = 28),
        axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5),
        legend.position = "none") +
  geom_point(size = 5, position = position_dodge(width = 0.4)) +
  geom_errorbar(aes(ymin = ci_lower, ymax = ci_upper), 
                width = 0.2, position = position_dodge(width = 0.4)) +
  # scale_color_manual(values = c("black", "#00BFC4", "#F8766D", rep("black", 4))) +
  # scale_shape_manual(values = c(17, 15, 19, rep(17, 4))) +
  scale_color_manual(values = c("black", "#00BFC4", rep("gray", 2), "#F8766D", rep("black", 4))) +
  scale_shape_manual(values = c(17, 15, rep(17, 2), 19, rep(17, 4))) +
  labs(title = "Factor scores by character",
       x = "Character",
       y = "Mean factor score") # 1000 by 500
```


## Studies 3-4

```{r s34 all no rotation, include = F}
# make combined dataset
d34_all <- d3_all %>% rownames_to_column("subid") %>%
  full_join(d4_all %>% rownames_to_column("subid")) %>%
  column_to_rownames("subid")

# examine scree plot
fa.parallel(d34_all)

# run EFA without rotation with N factors
efa_d34_all_unrotated <- fa(d34_all, 13, rotate = "none",
                           cor = chosenCorType, fm = "minres")
print(efa_d34_all_unrotated)

# examine eigenvalues and variance explained
efa_d34_all_unrotated_eigenvalues <- print(efa_d34_all_unrotated)$Vaccounted %>%
  t() %>%
  data.frame()

# count factors with eigenvalues > 1 and variance explained > 5%
efa_d34_all_unrotated_nfactors <- efa_d34_all_unrotated_eigenvalues %>%
  filter(SS.loadings > 1, Proportion.Explained > 0.05) %>%
  count() %>%
  as.numeric()
efa_d34_all_unrotated_nfactors
```

```{r s34 all rotation, include = F}
efa_d34_all_rotated_max <- fa(d34_all, 13, rotate = chosenRotType,
                           cor = chosenCorType, fm = "minres")

efa_d34_all_rotated <- fa(d34_all, efa_d34_all_unrotated_nfactors, rotate = chosenRotType,
                           cor = chosenCorType, fm = "minres")

# check that each of these factors is the dominant factor for at least one mental capacity item
efa_d34_all_rotated_loadings <- fa.sort(loadings(efa_d34_all_rotated)[]) %>%
  data.frame() %>%
  rownames_to_column("capacity") %>%
  gather(factor, loading, -capacity) %>%
  mutate(loading_abs = abs(loading)) %>%
  group_by(capacity) %>%
  top_n(1, loading_abs) %>%
  ungroup()
efa_d34_all_rotated_loadings

# drop any factors where n < 1
efa_d34_all_rotated_loadings %>% 
  count(factor) %>% 
  filter(n > 0)

# set number of factors to extract
nfactors_d34_all <- efa_d34_all_rotated_loadings %>% 
  count(factor) %>% 
  filter(n > 0) %>%
  nrow()
nfactors_d34_all
```

```{r s34 all varimax rotation, include = F}
# run EFA with rotation with N factors
efa_d34_all_rotatedN <- fa(d34_all, nfactors_d34_all, 
                          rotate = chosenRotType, cor = chosenCorType, fm = "minres",
                          scores = "tenBerge", missing = TRUE) # impute missing values
print(efa_d34_all_rotatedN)

# get loadings for each factor
efa_d34_all_rotatedN_loadings <- loadings(efa_d34_all_rotatedN)[] %>%
  data.frame() %>% 
  rownames_to_column(var = "capacity")
```

```{r s34 loadings table, include = F}
data.frame(loadings(fa.sort(efa_d34_all_rotatedN))[]) %>%
  rownames_to_column("capacity") %>%
  mutate_at(vars(starts_with("M")), funs(round2))
```

```{r s34 figure setup, include = F}
scores_s34_plotting <- d3 %>% 
  select(subid, age_group, character) %>% 
  distinct() %>% 
  mutate(subid = paste(character, subid, sep = "_")) %>%
  full_join(d4 %>% 
              select(subid, age_group, character) %>% 
              distinct() %>% 
              mutate(subid = paste(character, subid, sep = "_"))) %>%
  full_join(efa_d34_all_rotatedN$scores %>% 
              data.frame() %>% 
              rownames_to_column("subid")) %>%
  mutate(character = factor(character)) %>%
  rename(score_F1 = MR1, score_F2 = MR2, score_F3 = MR3) %>%
  filter(!is.na(score_F1), !is.na(score_F2), !is.na(score_F3), !is.na(age_group)) %>%
  gather(factor, score, starts_with("score_")) %>%
  mutate(factor = factor(factor)) %>%
  multi_boot(column = "score",
             summary_groups = c("age_group", "character", "factor"),
             statistics_functions = c("mean", "ci_lower", "ci_upper"))
```

```{r s34 figure factor scores by age group, fig.width = 12, fig.height = 6}
# plot
ggplot(scores_s34_plotting %>%
         ungroup() %>%
         mutate(character = factor(character, 
                                   levels = c("computer", "robot", "doll", "teddy_bear",
                                              "beetle", "bird", "mouse", "goat", "elephant"),
                                   labels = c("computer", "robot", "doll", "teddy bear",
                                              "beetle", "bird", "mouse", "goat", "elephant")),
                factor = factor(factor,
                                levels = c("score_F2", "score_F1", "score_F3"),
                                labels = c("Social-emotional", "Bodily", "Perceptual-cognitive")),
                age_group = factor(age_group,
                                  levels = c("children_46", "children_79"),
                                  labels = c("4-6y", "7-9y"))),
       aes(x = character, y = mean, color = character, shape = age_group)) +
  facet_wrap(~ factor, ncol = 3) +
  theme_bw() +
  theme(text = element_text(size = 28),
        axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5),
        legend.position = "bottom") +
  geom_point(size = 5, position = position_dodge(width = 0.4)) +
  geom_errorbar(aes(ymin = ci_lower, ymax = ci_upper), 
                width = 0.2, position = position_dodge(width = 0.4)) +
  # scale_color_manual(values = c("black", "#00BFC4", "#F8766D", rep("black", 4))) +
  # scale_shape_manual(values = c(17, 15, 19, rep(17, 4))) +
  scale_color_manual(values = c("black", "#00BFC4", rep("gray", 2), "#F8766D", rep("black", 4)),
                     guide = FALSE) +
  labs(title = "Factor scores by character and age group",
       x = "Character",
       y = "Mean factor score",
       shape = "Age group: ") # 1000 by 500
```

# Factor scores by age

## Study 1

```{r s1 factor scores by age setup, fig.width = 12, fig.height = 6}
scores_s1_plotting <- d1 %>% 
  select(subid, age, character) %>% 
  distinct() %>% 
  mutate(subid = paste(character, subid, sep = "_")) %>%
  full_join(efa_d1_all_rotatedN$scores %>% 
              data.frame() %>% 
              rownames_to_column("subid")) %>%
  mutate(character = factor(character)) %>%
  rename(score_F1 = MR1, score_F2 = MR2, score_F3 = MR3) %>%
  filter(!is.na(score_F1), !is.na(score_F2), !is.na(score_F3), !is.na(age)) %>%
  gather(factor, score, starts_with("score_")) %>%
  mutate(factor = factor(factor))

ggplot(scores_s1_plotting %>%
         ungroup() %>%
         mutate(factor = factor(factor,
                                levels = c("score_F2", "score_F1", "score_F3"),
                                labels = c("Social-emotional",
                                           "Bodily",
                                           "Perceptual-cognitive"))),
       aes(x = age, y = score, color = character, fill = character, shape = character)) +
  facet_wrap("factor", ncol = 3) +
  theme_bw() +
  theme(text = element_text(size = 28),
        legend.position = "bottom") +
  # geom_smooth(method = "loess", alpha = 0.4) +
  geom_smooth(method = "lm", alpha = 0.4) +
  geom_point(size = 2) +
  scale_shape_manual(values = c(19, 15)) +
  labs(title = "Factor scores by adults' age",
       # subtitle = "Adults (Study 1)\n",
       x = "Age (years)",
       y = "Factor score") # 1000 by 500
```

## Study 2

```{r s2 factor scores by age setup, fig.width = 12, fig.height = 6}
scores_s2_plotting <- d2 %>% 
  select(subid, age, character) %>% 
  distinct() %>% 
  mutate(subid = paste(character, subid, sep = "_")) %>%
  full_join(efa_d2_all_rotatedN$scores %>% 
              data.frame() %>% 
              rownames_to_column("subid")) %>%
  mutate(character = factor(character)) %>%
  rename(score_F1 = MR1, score_F2 = MR2, score_F3 = MR3) %>%
  filter(!is.na(score_F1), !is.na(score_F2), !is.na(score_F3), !is.na(age)) %>%
  gather(factor, score, starts_with("score_")) %>%
  mutate(factor = factor(factor))

ggplot(scores_s2_plotting %>%
         ungroup() %>%
         mutate(factor = factor(factor,
                                labels = c("Social-emotional",
                                           "Bodily",
                                           "Perceptual-cognitive"))),
       aes(x = age, y = score, color = character, fill = character, shape = character)) +
  facet_wrap("factor", ncol = 3) +
  theme_bw() +
  theme(text = element_text(size = 28),
        legend.position = "bottom") +
  # geom_smooth(method = "loess", alpha = 0.4) +
  geom_smooth(method = "lm", alpha = 0.4) +
  geom_point(size = 2) +
  scale_shape_manual(values = c(19, 15)) +
  labs(title = "Factor scores by children's age",
       # subtitle = "Children (Study 2)\n",
       x = "Age (years)",
       y = "Factor score") # 1000 by 500
```

## Studies 1-2

```{r s12 scatter plus mean scores by age setup, fig.width = 10, fig.height = 6}
tempA <- d2 %>% 
  select(subid, age, character) %>% 
  distinct() %>% 
  mutate(subid = paste(character, subid, sep = "_")) %>%
  full_join(efa_d12_all_rotatedN$scores %>% 
              data.frame() %>% 
              rownames_to_column("subid")) %>%
  mutate(character = factor(character)) %>%
  rename(score_F1 = MR1, score_F2 = MR2, score_F3 = MR3) %>%
  filter(!is.na(score_F1), !is.na(score_F2), !is.na(score_F3), !is.na(age)) %>%
  gather(factor, score, starts_with("score_")) %>%
  mutate(factor = factor(factor,
                         labels = c("Social-emotional",
                                    "Bodily",
                                    "Perceptual-cognitive")))

tempB <- scores_s12_plotting %>%
  filter(age_group == "adults") %>%
  ungroup() %>%
  mutate(factor = factor(factor,
                         labels = c("Social-emotional",
                                    "Bodily",
                                    "Perceptual-cognitive")),
         age = 11) 

ggplot(tempA,
       aes(x = age, y = score, color = character, fill = character, shape = character)) +
  facet_wrap("factor", ncol = 3) +
  theme_bw() +
  theme(text = element_text(size = 28),
        axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1),
        legend.position = "bottom") +
  # geom_smooth(method = "loess", alpha = 0.4) +
  geom_smooth(method = "lm", alpha = 0.4) +
  geom_point(size = 2) +
  geom_point(data = tempB, aes(y = mean),
             size = 4, position = position_dodge(width = 0.6)) +
  geom_errorbar(data = tempB, aes(ymin = ci_lower, ymax = ci_upper, y = mean), width = 0.4,
                position = position_dodge(width = 0.6)) +
  scale_shape_manual(values = c(19, 15)) +
  scale_x_continuous(breaks = c(7:11), labels = c("7y", "8y", "9y", "10y", "adults")) +
  labs(title = "Factor scores by age",
       # subtitle = "Children (Study 2)\n",
       x = "Age",
       y = "Factor score") # 1000 by 500
```

## Studies 3-4

```{r s34 factor scores by age setup, fig.width = 10, fig.height = 20}
scores_s34_plotting <- d3 %>%
  select(age_group, subid, age, character) %>%
  distinct() %>%
  mutate(subid = paste(character, subid, sep = "_")) %>%
  full_join(d4 %>%
              select(age_group, subid, age, character) %>%
              distinct() %>%
              mutate(subid = paste(character, subid, sep = "_"))) %>%
  full_join(efa_d34_all_rotatedN$scores %>%
              data.frame() %>%
              rownames_to_column("subid")) %>%
  mutate(character = factor(character)) %>%
  mutate(age = ifelse(age < 3.5, NA, age)) %>%
  rename(score_F1 = MR1, score_F2 = MR2, score_F3 = MR3) %>%
  filter(!is.na(score_F1), !is.na(score_F2), !is.na(score_F3), !is.na(age)) %>%
  gather(factor, score, starts_with("score_")) %>%
  mutate(factor = factor(factor))

ggplot(scores_s34_plotting %>%
         ungroup() %>%
         mutate(factor = factor(factor,
                                levels = c("score_F3", "score_F1", "score_F2"),
                                labels = c("Social-emotional",
                                           "Bodily",
                                           "Perceptual-cognitive")),
                character = factor(character,
                                   levels = c("computer", "robot", "doll", "teddy_bear",
                                              "beetle", "bird", "mouse", "goat", "elephant"))),
       # aes(x = age, y = score, color = character, fill = character, shape = character)) +
       aes(x = age, y = score, gropu = age_group)) +
  # facet_wrap("factor", ncol = 3) +
  # facet_grid(factor ~ character) +
  facet_grid(character ~ factor) +
  theme_bw() +
  theme(text = element_text(size = 28),
        legend.position = "none") +
  # geom_smooth(method = "loess", alpha = 0.4) +
  geom_smooth(method = "lm", alpha = 0.4) +
  # geom_smooth(method = "lm", alpha = 0.4, formula = y ~ poly(x, 2)) +
  # geom_smooth(method = "lm", alpha = 0.4, formula = y ~ poly(x, 3)) +
  geom_point(size = 2) +
  scale_x_continuous(breaks = seq(2, 12, 2)) +
  # scale_fill_manual(values = c("black", "#00BFC4", rep("gray", 2), "#F8766D", rep("black", 4))) +
  # scale_color_manual(values = c("black", "#00BFC4", rep("gray", 2), "#F8766D", rep("black", 4))) +
  # scale_shape_manual(values = c(17, 15, rep(17, 2), 19, rep(17, 4))) +
  labs(title = "Factor scores by children's age",
       # subtitle = "Children (Studies 3-4)\n",
       x = "Age (years)",
       y = "Factor score") # 1000 by 500
```

